Using the World Wide Web for Teaching Statistics

This document contains problems that can be used in an introductory statistics course. The problems are grouped into the following categories.

Organizing Data

Numerical Description of Data

Binomial Distribution

Normal Distribution

Sampling Distribution

Confidence Intervals for Proportions

Tests of Hypothesis about Proportion

Comparison of Two Proportions

Confidence Intervals for Mean

Tests about Mean

Comparison of Means

Chi Square Test

Linear Regression and Correlation

The following sites have useful resources for teaching statistic.

The Dataset and Story Library: http://lib.stat.cmu.edu/DASL/

Data Surfing: http://it.stlawu.edu/~rlock/datasurf.html

StatLib Dataset Archive: http://lib.stat.cmu.edu/datasets/

Java Applets for Statistics: http://www.stat.duke.edu/sites/java.html

Multimedia Statistics Page: http://www.berrie.dds.nl/index.html

Rice Virtual Lab in Statistics: http://www.ruf.rice.edu/~lane/rvls.html

Journal of Statistics Education Data Archive: http://www.amstat.org/publications/jse/jse_data_archive.html

Organizing Data

1. In a survey of 1000 people, conducted in June 2002 by Strategy One/Colonial Williamsburg, they were asked what issues was most important to them out of the choices given in the table below.

Issue	Percentage of Response
Freedom of Speech	26
Access to affordable health care	20
Freedom of religion	19
Opportunity of economic advancement	12
Right to pursue an education	12
Freedom of press	3
Don’t know/none of the above	8

(Source: Survey One/Central Williamsburg, USA Today, August 13, 2002)

Draw a pie chart to describe the distribution.

2. 25 countries won medals in the 2002 Winter Olympics. The table below list them along with the total number of medals each won.

Country	Medals	Country	Medals
Germany	35	Croatia	4
USA	34	Korea	4
Norway	24	Bulgaria	3
Canada	17	Estonia	3
Austria	16	Great Britain	3
Russia	16	Australia	2
Italy	12	Czech Republic	2
France	11	Japan	2
Switzerland	11	Poland	2
China	8	Spain	2
Netherlands	8	Belarus	1
Finland	7	Slovenia	1
Sweden	6

(Source: CNNSI.com http://sportsillustrated.cnn.com/olympics/2002/current_medal_tracker/)

(a) Draw a pie chart to describe the distribution. What problems do you encounter?

(b) Can you find a way to organize the data so that the graph is more successful?

3. 202 countries participated in 2004 Summer Olympics, and 75 countries won medals. The table below list top 25 countries with the total number of medals won.

Country	Medals	Country	Medals
USA	103	Romania	19
Russia	92	Spain	19
China	63	Hungary	17
Australia	49	Greece	16
Germany	48	Belarus	15
Japan	37	Canada	12
France	33	Bulgaria	12
Italy	32	Brazil	10
South Korea	30	Turkey	10
Great Britain	30	Poland	10
Cuba	27	Thailand	8
Ukraine	23	Denmark	8
Netherlands	22

(Source: CNNSI.com http://sportsillustrated.cnn.com/olympics/2004/medaltracker/medalTrackerByTotal.html)

a. Draw a pie chart to describe the distribution. What problems do you encounter?

b. Can you find a way to organize the data so that the graph is more successful?

4. The following table, based on the American Chamber of Commerce Researchers Association Survey for the second quarter of 2002, gives the prices (in dollars) of five items in 25 urban areas across the United States.

City	Apartment Rent	Phone Bill	Price of Gasoline	Visit to Doctor	Price of Beer
Montgomery (AL)	$576	$22.28	$1.335	$52.33	$7.88
Juneau (AK)	1020	18.26	1.584	88.67	8.12
Tucson (AZ)	689	21.03	1.347	54.80	7.79
Sacramento (CA)	749	16.99	1.643	70.00	6.99
San Diego (CA)	1306	24.57	1.632	75.20	7.99
Denver (CO)	891	23.10	1.343	71.8	6.90
Hartford (CT)	896	22.39	1.419	80.25	7.15
Jacksonville (FL)	810	20.31	1.419	63.80	7.15
Bloomington (IN)	678	19.95	1.402	56.67	6.99
New Orleans (LA)	798	26.06	1.351	56.20	6.56
Boston (MA)	1248	24.41	1.405	78.00	7.21
Grand Rapids (MI)	678	22.40	1.499	59.20	8.03
Minneapolis (MN)	815	25.16	1.366	72.20	7.49
Springfield (MO)	568	18.25	1.309	63.72	7.89
Billings (MT)	550	30.45	1.449	70.75	7.09
Buffalo (NY)	714	33.71	1.413	53.00	7.03
Charlotte (NC)	540	21.07	1.359	58.00	7.03
Akron (OH)	686	21.16	1.519	59.40	7.29
Oklahoma City (OK)	579	23.04	1.308	60.02	6.94
Portland (OR)	753	20.92	1.403	72.40	7.69
Philadelphia (PA)	1282	21.12	1.360	62.50	8.57
Austin (TX)	1025	19.20	1.299	68.33	6.78
Richmond (VA)	769	26.15	1.317	59.80	6.37
Spokane (WA)	593	18.49	1.305	61.80	6.89
Charleston (WV)	606	27.08	1.423	64.67	7.01

Explanation of variables

Apartment Rent: Monthly rent of an unfurnished 2-bedroom apartment (excluding all utilities except water), 1 ½ or 2 baths, approximately 950 square feet.

Phone Bill: Monthly telephone charges for a private residential line (customer owns instruments).

Price of Gasoline: Price of one gallon regular unleaded, national brand.

Visit to doctor: General practitioner’s routine examination of patient.

Price of Beer: Heineken’s 6-pack, 12-oz. containers, excluding deposit.

a. Prepare frequency distributions for the five variables.

b. Construct the relative frequency and percentage distribution for the five variables.

c. Draw histograms.

5. The table below shows the average SAT scores for each of the 50 states and District of Columbia for 1990 and 2000.

State	1990	2000
Alabama	1079	1114
Alaska	1015	1034
Arizona	1041	1044
Arkansas	1077	1117
California	1002	1015
Colorado	1067	1071
Connecticut	1002	1017
Delaware	1006	998
D.C	950	980
Florida	988	998
Georgia	951	974
Hawaii	985	1007
Idaho	1066	1081
Illinois	1089	1154
Indiana	972	999
Iowa	1172	1189
Kansas	1129	1154
Kentucky	1089	1098
Louisiana	1088	1120
Maine	991	1004
Maryland	1008	1016
Massachusetts	1001	1024
Michigan	1063	1126
Minnesota	1110	1175
Mississippi	1090	1111
Missouri	1089	1149
Montana	1082	1089
Nebraska	1121	1131
Nevada	1022	1027
New Hampshire	1028	1039
New Jersey	993	1011
New Mexico	1100	1092
New York	985	1000
North Carolina	948	988
North Dakota	1157	1197
Ohio	1048	1072
Oklahoma	1095	1123
Oregon	1024	1054
Pennsylvania	987	995
Rhode Island	986	1005
South Carolina	942	966
South Dakota	1150	1175
Tennessee	1102	1116
Texas	979	993
Utah	1121	1139
Vermont	1000	1021
Virginia	997	1009
Washington	1024	1054
West Virginia	1034	1037
Wisconsin	1111	1181
Wyoming	1072	1090

(Source: College Entrance Examination Board, 2001)

a. Use graphs to display the two SAT score distributions. How has the distribution of average state scores changed over the decade?

b. Compute the paired difference by subtracting the 1990 score from the 200 score for each state. Summarize these differences with a graph.

Numerical Description of Data

6. In an advertisement in USA Today (July 9, 2001), the company Net2Phone listed its long distance rates to 24 of the 250 countries to which it offers service.

Country	Cost per Minute (cents)	Country	Cost per Minute (cents)
Belgium	7.9	Italy	9.9
Chile	17	Japan	7.9
Canada	3.9	Mexico	16
Colombia	9.9	Pakistan	49
Dominican Republic	15	Philippines	49
Finland	9.9	Puerto Rico	21
France	7.9	Singapore	11
Germany	7.9	South Korea	9.9
Hong Kong	7.9	Taiwan	9.9
India	49	United Kingdom	7.9
Ireland	7.9	United States	3.9
Israel	8.9	Venezuela	22

a. Make a graphical display of these rates.

b. Find the mean and the median.

c. Find the standard deviation.

7. The U.S. Department of Transportation collects data on the amount of gasoline sold in each state. The following data show the per capita (gallons used per person) consumption in the year 2000. Using appropriate graphical displays and summary statistics, write a report on the gasoline use by state in the year 2000.

Alabama	544.71	Montana	548.5
Alaska	433.08	Nebraska	508.28
Arizona	452.82	Nevada	446.17
Arkansas	532.82	NH	542.86
CA	422.65	NJ	474.28
Colorado	461.90	NM	474.28
CT	431.04	New York	551.18
Delaware	481.45	NC	296.66
Florida	542.36	ND	513.3
Georgia	452.82	Ohio	574.83
Hawaii	327.27	OK	457.63
Idaho	500.34	Oregon	520.42
Illinois	406.66	PA	441.44
Indiana	518.7	RI	410.31
Iowa	534.7	SC	381.86
Kansas	511.34	SD	555.06
Kentucky	510.9	TN	586.58
LA	522.12	Texas	515.17
Maine	542.36	Utah	498.66
Maryland	542.82	Vermont	456.27
Mass	438.1	Virginia	584.03
Michigan	502.77	WA	506.92
MN	528.06	WV	450.4
MS	559.29	WI	462
Missouri	563.56	Wyoming	462.67

8. The Gallup Poll conducted a representative telephone survey during the fist quarter of 1999. Among their reported results was the following table concerning the preferred political party affiliation of respondents and their ages?

	Rep.	Dem.	Ind.	Total
18-29	241	351	409	1001
30-49	299	330	370	999
50-64	282	341	375	998
65+	279	382	343	1004
Total	1101	1404	1497	4002

a. What percent of people surveyed were Republicans?

b. Do you think this might be a reasonable estimate of the percentage of all voters who are Republicans? Explain.

c. What percent of people surveyed were under 30 or over 65?

d. What percent of people were Independents under the age of 30?

e. What percent of Independents were under 30?

f. What percent of people under 30 were Independents?

9. The following table gives the number of home runs hit during the 2002 season by all of the baseball teams in the American League

Team	Home Runs	Team	Home Runs	Team	Home Runs
Anaheim	152	Texas	230	Tampa Bay	133
Boston	177	Chicago	217	Cleveland	192
New York	223	Toronto	187	Detroit	124
Seattle	152	Oakland	205	Baltimore	165
Minnesota	167	Kansas City	140

a. Find the mean and median.

b. Find the standard deviation

10. The following table shows the number of stolen bases (SB) by each of the 16 National League baseball teams during the 2002 season

Team	SB	Team	SB	Team	SB
Colorado	103	Montreal	118	Cincinnati	116
St. Louis	86	Florida	177	Milwaukee	94
Arizona	92	Atlanta	76	San Diego	71
San Francisco	74	Philadelphia	104	Chicago	63
Los Angeles	96	New York	87	Pittsburgh	86
Houston	71

a. Find the mean and median.

b. Find the standard deviation.

Binomial Distribution

11. According to a survey by Food Processing, 85% of Americans say they eat home-cooked meals three or more times per week (Time, October 7, 2002). Suppose that this result is true for the current population of Americans.

a. Let X be a binomial random variable that denotes the number of Americans in a random sample of 12 who say they eat home-cooked meals three or more times per week. What are the possible values that X can assume?

b. Find the probability that in a random sample of 10 shoppers, exactly 4 faithfully buy the same cereal.

12. During the hard economic times, people switch between brands while shopping and rarely stick to one brand. According to an Insight Express online survey of hoppers, only 24% faithfully buy a favorite cereal (CBS.MarketWatch.com, October 1, 2002). Assume that this percentage is true for the current population of all shoppers.

a. Let X be a binomial random variable that denotes the number who faithfully buy the same cereal in a random sample of 10 shoppers. What are the possible values that X can assume?

b. Find the probability that in a random sample of 10 shoppers, exactly 4 faithfully buy the same cereal.

13. In a poll of 12-18 year-old females conducted by Harris Interactive for the Gillette Company, 40% of the young females said that they expected the United States to have a female president within 10 years (USA Today, October 1, 2002). Assume that this result is true for the current population of all 12-to 18-year-old females. Suppose a random sample of 16 females from this age group is selected. Find the probability that the number of young females in this sample who expect a female president within 10 years is

a. at least 9 b. at most 5 c. between 6 to 9

14. According to a 2001 study of college students conducted by Harvard University’s School of Public Health, 34.9% of the male students surveyed said they got drunk three or more times in the past 30 days. (USA Today, April 3, 2002). Assuming that this result holds true for all male college students, find the probability that in a random sample of 10 male college students, the number of students who got drunk three or more times in the past 30 days is

a. exactly 4 b. none c. exactly 8

Normal Distribution

15. The U.S. Bureau of Labor Statistics conducts periodic surveys to collect information on the labor market. According to one such survey, the average earnings of workers in retail trade were$10 per hour in August 2002 (Bureau of Labor Statistics News, September 18, 2002). Assume that the hourly earnings of such workers in August 2002 had a normal distribution with a mean of $10 and a standard deviation of $1.10. Find the probability that the hourly earnings of a randomly selected retail trade worker in August 2002 were

a. more than $12 b. between $8.50 and $10.80

16. According to a survey by the Kaiser Family Foundation, employers paid an average of $7954 per employee in annual premiums to provide family health coverage for their employees, and each worker paid and average of $2084 toward these premiums (USA Today, September 6, 2002). Assume that the current annual premiums paid by all workers for family health coverage are normally distributed with a mean of $2084 and a standard deviation of $300.

a. Find the probability that a randomly selected worker pays more than $2500 per year toward the family health coverage premium.

b. What percentage of such workers are paying between $1800 and $2400 per year toward such premiums?

17. In a Visa USA poll of Americans, participants were asked which of the following had taught them the most about money management: school or mistakes. Sixty-four percent of the persons polled said that mistakes had taught them the most (USA Today, May 16, 2002). Assume that this result is true for the current population of all Americans. Find the probability that in a random sample of 400 Americans, the number who will say that mistakes have taught them the most about money management is

a. exactly 250 b. 260 to 272 c. at most 244

18. According to a survey by Money magazine, 27% of women expect to support their parents financially (USA Today, June 19, 2002). Assume that this percentage holds true for the current population of all women. Suppose that a random sample of 300 women is taken.

a. Find the probability that exactly 79 of the women in this sample expect to support their parents financially.

b. Find the probability that at most 74 of the women in this ample expect to support their parent financially.

c. What is the probability that between 75 and 89 of the women in this sample expect to support their parents financially?

Sampling Distribution

19. According to International Communications Research for Cingular Wireless, men talk an average of 594 minutes per month on their cell phones (USA Today, July 29, 2002). Assume that currently 594 minutes with a standard deviation of 160 minutes. Let X be the mean time spent per month talking on their cell phones by a random sample of 400 men who own cell phones. Find the mean and standard deviation of X.

20. According to the U.S. Bureau of Labor Statistics estimates, the average earnings of construction workers were $18.96 per hour in August 2002 (Bureau of Labor Statistics News, September 18, 2002). Assume that the current earnings of all construction workers are normally distributed with a mean of $18.96 per hour and a standard deviation of $3.60 per hour. Find the probability that the mean hourly earning of a random sample of 25 construction workers is

a. between $18 and $20 per hour

b. within $1 of the population mean

c. greater that the population mean by $1.50

21. According toCardWeb.com, the average credit card debt per household was $8367 in 2001 (USA Today, April 29, 2002). Assume that the probability distribution of all such current debts is skewed to the right with a mean of $8367 and a standard deviation of $8367 and a standard deviation of $2400. Find the probability that the mean of a random sample of 225 such debts is

a. between $8100 and$8500

b. within $200 of the population mean

c. greater that the population mean by $300 or more

22. A Maritz poll of adult drivers conducted in July 2002 found that 45% of them “often” or “sometimes” eat or drink while driving (USA Today, October 23, 2002). Assume that 45% of all current adult drivers “often” or “sometimes” eat or drink while driving. Let p be the proportion of adult drivers in a sample of 400 who behave this way. Find the mean and standard deviation of p and describe the shape of its sampling distribution.

23. In a 2002 USA TODAY-CNN-Gallup poll, 37% of taxpayers said that the income tax they had to pay was not fair (USA Today, April 15, 2002). Assume that this percentage is true for the current population of all taxpayers. Let p be the proportion of taxpayers in a random sample of 300 who will say that the income tax they have to pay is not fair. Calculate the mean and standard deviation of p and comment on the shape of its sampling distribution.

24. In a Retirement Confidence survey of retired people, 51% said that retirement is better than they had expected (U.S. News & World Report, June 3, 2002). Assume that this percentage is true for the current population of all retirees. Let p be the proportion of retirees in a random sample of 225 who hold this opinion. Calculate the mean and standard deviation of p and describe the shape of its sampling distribution.

25. According to a 2002 survey by America Online, mothers with children under 18 years of age spent an average of 16.87 hours per week online (USA Today, May 7, 2002). Assume that the mean time spent online by all current mothers with children under 18 years of age is 16.87 hours per week with a standard deviation of 5 hours per week. Find the probability that the mean time spent online per week by a random sample of 100 such mothers is

a. greater that 17 hours

b. between 16.5 and 17.5 hours

c. within .75hour of the population mean

d. less than the population mean by .75 hour or more

Confidence Intervals for Proportions

26. Due to sluggish economic conditions, the percentage of companies that host holiday parties for their employees have declined. According to a survey by Hewitt Associates, 64% of the companies hosted holiday parties in 2002 (USA Today, December 2, 2002). Assume that this result is based on a random sample of 400 U.S. companies.

a. Find a 98% confidence interval for the proportion of all U.S. companies who hosted holiday parties in 2002.

b. Explain why we need to make the confidence interval. Why can we not say that 64% of all U.S. companies hosted parties in 2002?

27. A May 2002 Gallup Poll found that only 8% of a random sample of 1012 adults approved of attempts to clone a human.

a. Find the margin of error for this poll if we want 95% confidence in our estimate of the percent of American adults who approve of cloning humans.

b. Explain what that margin of error means.

c. If we only need to be 90% confident, will the margin of error be larger or smaller? Explain.

d. Find that margin of error.

e. In general, if all other aspects of the situation remain the same, would smaller samples produce smaller or larger margins of error?

28. In the 1992 U.S. presidential election, Bill Clinton received 43% of the vote compared with 38% for George Bush, and 19% for Ross Perot. Suppose we had taken a random sample of 100 voters in an exit poll and asked them for whom they had voted.

a. Would you always get 43 votes for Clinton, 38 for Bush, and 19 for Perot in a sample of 100? Why or why not?

b. In 95% of such polls, our sample proportion of voters for Clinton should be between what two values?

c. In 95% of such polls, the sample proportion of Perot votes should be between what two numbers?

d. Would you expect the sample proportion of Perot votes to vary more, less, or about the same as the sample proportion of Bush votes? Why?

29. In May of 200, the Pew Research Foundation sampled 1593 respondents and asked how they obtain news. In Pew’s report, 33% of respondents say that they now obtain news from the Internet at least once a week.

a. Pew reports a margin of error of 3% for this result. Explain what the margin of error means.

b. Pew also asked about investment information, and 21% of respondents reported that the Internet is their main source of this information. When limited to the 780 respondents who identified themselves as investors, the percent who rely on the Internet rose to 28%. How would you expect the margin of error for this statistic to change in comparison with the margin of error for the percentage of all respondents?

c. When restricted to the 239 active traders in the sample, Pew reports that 45% rely on the Internet for investment information. Find a confidence interval for this statistic.

d. How does the margin of error for your confidence interval compare with the values in parts a and b? Explain why.

30. In May of 2002, the Gallup Organization asked a random sample of 537 American adults this question:

If you could choose between the following two approaches, which do you think is the better penalty for murder, the death penalty or life imprisonment, with absolutely no possibility of parole?

Of those polled, 52% chose the death penalty.

a. Find a 95% confidence interval for the percentage of all American adults who favor the death penalty.

b. Based on your confidence interval, is it clear that the death penalty has majority support? Explain.

c. If pollsters wanted to follow up on this poll with another survey that could determine the level of support for the death penalty to within 2% with 98% confidence, how many people should they poll?

Tests of Hypothesis about Proportion

31. During the 2000 season, the home team won 138 of the 240 regular season National Football League games. Is this strong evidence of a home field advantage in professional football? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.

32. In 2000, 19 million registered voters failed to vote in the presidential election. According to the U.S. Census Bureau’s Current Population Survey in November 2000, the most frequently given reason for not voting was “too busy,” cited by 20.9% of the respondents (USA Today, April 15, 2002). Suppose that a random sample of 250 registered voters who did not vote in the November 2002 midterm elections showed that 18.1% of them stated the main reason for not voting was that they were too busy. At the 5% level of significance, can you conclude that the percentage of the registered voters who did not vote in November 2002 because they were too busy was less than 20.9%?

33. According to a 2002 survey conducted by Harris Interactive for lawyers.com, 47% of Americans dream of owning a business (USA Today, September 10,2002). Assume that this result was true for the population of Americans in 2002. A recent random sample of 100 Americans found that 430 of 5them dream of owning a business. Test at the 5% significance level if the current percentage of Americans who dream of owning a business is different from 47%.

34. In a 2002 Affluent Americans and Their Money survey of “affluent” Americans (having an annual household income of $75,000 of more) conducted for Money magazine by RoperASW, 32% of the respondents indicated that they would have a serious problem paying an unexpected bill of $5000 (Money, Fall 2002). In a recent random sample of 1100 households with annual income of $75,000 or more, 396 said that they would have a serious problem paying an unexpected bill of $5000.

a. Test at the 2.5% significance level, whether the company should market this yogurt?

b. What will your decision be in part (a) if the probability of making a Type I error is zero? Explain.

Comparison of Two Proportions

35. A Vermont study published in December 2001 by the American Academy of Pediatrics examined parental influence on teenagers’ decisions to smoke. A group of students who had never smoked were questioned about their parents’ attitudes toward smoking. These students were questioned again two years later to see if they had started smoking. The researchers found that among the 284 students who indicated that their parents disapproved of kids smoking, 54 had become established smokers. Among the 41 students who initially said their parents were lenient about smoking, 11 became smokers. Do these data provide strong evidence that parental attitude influences teenagers’ decisions about smoking?

a. What kind of design did the researchers use?

b. Write appropriate hypotheses.

c. Are the assumptions and conditions necessary for inference satisfied?

d. Test the hypothesis and state your conclusion.

e. Explain in this context what your p-value means.

f. If that conclusion is actually wrong, which type of error did you commit?

36. The August 2001 issue of Pediatrics reported on a study of adolescent suicide attempts. Questionnaires were given to 6577 middle and high school students, 214 of whom were adopted. Of the 6577 students 213 youngsters said they had attempted suicide within the last year: 16 of those who were adopted and 197 of those who were not. Does this indicate a significantly different rate of suicide among adopted teens?

a. Test an appropriate hypothesis and state your conclusion.

b. If you concluded there was a difference, estimate that difference with a confidence interval and interpret your interval in context.

37. Among 242 Cleveland area children born prematurely at low birth weights between 1977 and 1979, only 74% graduated from high school. Among a comparison group of 233 children of normal birth weight, 83% were high school graduates. (New England Journal of Medicine, 346, no. 3 [2002])

a. Find a 95% confidence interval for the difference in graduation rates between children of normal and very low birth weights. Be sure to check the appropriate assumption and conditions.

b. Does this provide evidence that premature birth may be a risk factor for not finishing high school? Use your confidence interval to test an appropriate hypothesis.

c. Suppose your conclusion is incorrect. Which type of error did you make?

Confidence Intervals for Mean

38. According to Money magazine, the average net worth of U.S. households in 2002 was $355,000 (Money, Fall 2002). Assume that this mean is based on a random sample of 500 households and that the sample standard deviation is $125,000. Find a 99% confidence interval for the 2002 mean net worth of all U.S.households.

39. According to a 2002 survey by America Online, mothers with children under age 18 spent an average of 16.87 hours per week online (USA Today, May 7, 2002). Suppose that this mean is based on a random sample of 1000 such mothers and that the standard deviation for this sample is 3.2 hours per week. Find a 95% confidence interval for the corresponding population mean for all such mothers.

40. According to Money magazine, the average price of new homes in the United States was $145,000 in 2002 (Money, Fall 2002). Assume that this mean is based on a random sample of 1000 new home sales and that the sample standard deviation is $24,000. Find a 95% confidence interval for the 2002 mean price of all such homes.

41. According to Money magazine, the average cost of a movie ticket in the United States was $5.70 in 2002 (Money, Fall 2002). Suppose that a random sample of 25 theaters in the United States yielded a mean movie ticked price of $5.70 with a standard deviation of $1.05. Assuming that movie ticket prices are normally distributed, find a 95% confidence interval for the mean price of movie tickets for all theaters in the United States.

Tests about Mean

42. In 1998, as an advertising campaign, the Nabisco Company announced a “1000 Chips Challenge,” claiming that every 18-ounce bag of their Chips Ahoy cookies contained at least 1000 chocolate chips. The students in a Statistics class at the Air Force Academy purchased some randomly selected bags of cookies, and counted the chocolate chips. Some of their data are given below. (Chance, 12, no. 1, 1999)

1219 1214 1087 1200 1419 1121 1325 1345

1244 1258 1356 1132 1191 1270 1295 1135

a. Find a 95% confidence interval for the average number of chips in bags of Chips Ahoy cookies.

b. What does this evidence say about Nabisco’s claim? Use your confidence interval to test an appropriate hypothesis and state your conclusion.

43. According to the U.S. Bureau of Labor Statistics, there were 8.1 million unemployed people aged 16 years and over in August 2002. The average duration of unemployment for these people was 16.3 weeks (Bureau of Labor Statistics News, September 6, 2002). Suppose that a recent random sample of 400 unemployed Americans aged 16 years and over gave a mean duration of unemployment of 16.9 weeks with a standard deviation of 4.2 weeks. Find the p-value for the hypothesis test with the alternative hypothesis that the current mean duration of unemployment for all unemployed Americans aged 16 years and over exceeds 16.3 weeks. Will you reject the null hypothesis at = .02?

44. According to an estimate, Americans spend an average of $226 per year to “look good,” buying personal-care products and services such as tooth whitener, hair dyes, and sessions at salons (Reader’s Digest, September 2002). Suppose that a recent random sample of 250 Americans showed that they spent an average of $238 on such products and services this year with a standard deviation of $77.

a. Find the p-value for the test of hypothesis with the alternative hypothesis that the current mean annual amount spent on such products and services differs from $226.

b. If = .01, would you reject the null hypothesis based on the p-value calculated in part a? What if = .02?

45. According to the International Communications Research for Cingular Wireless, women talked an average of 394 minutes per month on their cell phones in 2002 (USA Today, July 29, 2002). Suppose that a recent sample of 295 women who own cell phones showed that the mean time they spend per month talking on their cell phones is 402 minutes with a standard deviation of 81 minutes.

a. At the 2% level of significance, can you conclude that the mean time spent talking on their cell phones by all women who own cell phones is currently more that 394 minutes per month?

b. What is the Type I error in this case? What is the probability of making this error in part a?

46. According to Money magazine, the average cost of a visit to a doctor’s office in the United States was $60 in 2002 (Money, Fall 2002). Suppose that a recent random sample of 25 visits to doctors gave a mean of $63.50 and a standard deviation of $2.00. Using the 5% significance level, can you conclude that the current mean cost of a visit to a doctor’s office exceeds $60? Assume that such cost for all visits to doctors are normally distributed.

47. According to the U.S Bureau of Labor Statistics, production workers in the mining industry worked an average of 43.5 hours per week in June 2002 (Bureau of Labor Statistics News, September 6, 2002). A random sample of 24 production workers selected recently from a large mining company, Low Yield Mine, found that they work an average of 41.7 hours per week with a standard deviation of 1.3 hours per week. Assume that the weekly working hours of all these employees are normally distributed.

a. Suppose that the probability of making a Type I error is selected to be zero. Can you conclude that workers at Low Yield Mine work less than 4.35 hours per week? Answer without performing the five steps of a test of hypothesis.

b. Using the 5% level of significance, can you conclude that workers at Low Yield Mine work less than 43.5 hours per week?

Comparison of Means

48. In the 2002 National Geographic Society—RoperASW poll of geographic knowledge, young adults of 18 to 24 years of age from the United States and 8 other nations were asked to identify 11 countries on a numbered map of Asia (National Geographic, December 2002). The two highest-scoring nations were Germany, with an average of 6.7 correct identifications out of 11, and Sweden, with an average of 6.3 correct answers. Suppose that these means were based on random samples of 400 young adults from Germany and 600 from Sweden, and that the sample standard deviations of scores for Germany and Sweden were .7 and .8, respectively.

a. Let and be the population mean for Germany and Sweden, respectively. Find the point estimate of and its margin of error.

b. Find a 98% confidence interval for . Using the 5% level of significance, can you conclude that the mean score for all young adults from Germany is greater than that of all young adults from Sweden?

49. According to Smith Travel Research, the mean hotel room rates in the United States were $85.69 and $84.58 per day in 200 and 2001, respectively (USA Today, September 4, 2002). Suppose that these mean rates were based on random samples of 1000 hotel rooms for 2000 and 1100 hotel rooms for 2001; further assume that the standard deviations of these rates for the two samples were $18.50 and $18, respectively.

a. Let and be the mean rates for all hotel rooms in the United States in 200 and 2001, respectively. What are the point estimate of u1-u2 and its margin of error?

b. Find a 90% confidence interval for .

c. Test ate the 1% significance level whether the mean hotel room rate for 2000 was higher than that for 2001.

50. In June 2002, the Journal of Applied Psychology reported on a study that examined whether the content of TV shows influenced the ability of viewers to recall brand names of items featured in the commercials. The researchers randomly assigned volunteers to watch one of three programs, each containing the same nine commercials. One of the programs had violent content, another sexual content, and the third neutral content. After the shows ended the subjects were asked to recall the brands of products that were advertised. Results are summarized below.

	Violent	Sexual	Neutral
No. of subjects	108	108	108
Mean	2.08	1.71	3.17
St. Dev	1.87	1.76	1.77

a. Do the results indicate that viewer memory for ads may differ depending on the program content?

b. Is there evidence that viewer memory for ads may differ between programs with sexual content and those with neutral content?

51. In a full-page ad that ran in many U.S. newspapers in August 2002, a Canadian discount pharmacy listed costs of drugs that could be ordered from a Website in Canada. The table compares prices (in US$) for commonly prescribed drugs.

COST PER 100 PILLS

	United States	Canada	Percent Savings
Cardizem	131	83	37
Celebrex	136	72	47
Cipro	374	219	41
Pravachol	370	166	55
Premarin	61	17	72
Prevacid	252	214	15
Prozac	263	112	57
Tamoxifen	349	50	86
Vioxx	243	134	45
Zantac	166	42	75
Zocor	365	200	45
Zoloft	216	105	51

a. Find a 95% confidence interval for the average savings in dollars.

b. Find a 95% confidence interval for the average savings in Percent.

c. Which analysis do you think is more appropriate? Why?

52. Ever since Lou Gehrig developed amyotrophic lateral sclerosis (ALS), this deadly condition has been commonly known as Lou Gehrig’s disease. Some believe that ALS is more likely to strike athletes or the very fit. Columbia University neurologist Lewis P. Rowland recorded personal histories of 431 patients he examined between 1992 and 2002. He diagnosed 280 as having ALS; 38% of them had been varsity athletes. The other 151 had other neurological disorders, and only 26% of them had been varsity athletes. (Science News, Sept.28, 2002). Is there evidence that ALS is more common among athletes?

53. A study of the health behavior of school-aged children asked a sample of 15-year-olds in several different countries if they had been drunk at least twice. The results are shown in the table, by gender. Find a 95% confidence interval for the difference in the rates for males and females. Be sure to check the assumptions that support your chosen procedure, and explain what your interval means. (Health and Health Behavior Among Young people. Copenhagen: World Health Organization, 2000)

Percent of 15-Year-Olds Drunk at Least Twice

Country	Female	Male
Denmark	63	71
Wales	63	72
Greenland	59	58
England	62	51
Finland	58	52
Scotland	56	53
No. Ireland	44	53
Slovakia	31	49
Austria	36	49
Canada	42	42
Sweden	40	40
Norway	41	37
Ireland	29	42
Germany	31	36
Latvia	23	47
Estonia	23	44
Hungary	22	43
Poland	21	39
USA	29	34
Czech Rep.	22	36
Belgium	22	36
Russia	25	32
Lithuania	20	32
France	20	29
Greece	21	24
Switzerland	16	25
Israel	10	18

54. In March 2002, Consumer Reports listed the rate of return for several large cap mutual funds over the previous 3-year and 5-year periods. (“Large cap” refers to companies worth over $10 billion.)

Annualized Returns (%)

Fund Name	3-year	5-year
Ameristock	7.9	17.1
Clipper	14.1	18.2
Credit Suisse Strategic Value	5.5	11.5
Dodge & Cox Stock	15.2	15.7
Excelsior Value	13.1	16.4
Harbor Large Cap Value	6.3	11.5
ICAP Discretionary Equity	6.6	11.4
ICAP Equity	7.6	12.4
Neuberger Berman Focus	9.8	13.2
PBHG Large Cap Value	10.7	18.1
Pelican	7.7	12.1
Price Equity Income	6.1	10.9
USAA Cornerstone Strategy	2.5	4.9
Vanguard Equity Income	3.5	11.3
Vanguard Windsor	11.0	11.0

a. Find a 95% confidence interval for the difference in rate of return for the 3- and 5-year periods covered by these data. Clearly explain what your interval means.

b. It’s common for advertisements to carry the disclaimer that ”past returns may not be indicative of future performance,” but do these data indicate that there was an association between 3-year and 5-year rates of return?

Chi Square Test

55. In 2000, the Journal of American Medical Association published a study that examined a sample of pregnancies that resulted in the birth of twins. Births were classified as preterm with intervention (induced labor or cesarean), preterm without such procedures, or term or postterm. Researchers also classified the pregnancies by the level of prenatal medical care the mother received (inadequate, adequate, or intensive). The data, from the years 1995-97, are summarized in the table below. Figures are in thousands of births. (JAMA 284, 2000)

TWIN BIRTHS 1995-1997 (IN THOUSANDS)

	Preterm (induced or Cesarean)	Preterm (without procedures)	Term or postterm	Total
Intensive	18	15	28	61
Adequate	46	43	65	154
Inadequate	12	13	38	63
Total	76	71	131	278

Is there evidence of an association between the duration of the pregnancy and the level of care received by the mother?

56. The Gallup Poll conducted a representative telephone survey during the first quarter of 1999. Among the reported results was the following table concerning the preferred political party affiliation of respondents and their ages. Is there evidence of age-based differences in party affiliation in the United States?

	Republican	Democratic	Independent	Total
18-29	241	351	409	1001
30-49	299	330	370	999
50-64	282	341	375	998
65+	279	382	343	1004
Total	1101	1404	1497	4002

a. Will you conduct a test of homogeneity or independence? Why?

b. Test an appropriate hypothesis.

c. State your conclusion, including an analysis of differences you find (if any).

57. In January 2002, 725 people receiving outplacement assistance, with incomes of $60,000 to $150,000 were asked how long they could comfortably afford to be unemployed (Business Week, April 15, 2002). Eight percent said” less than three months,” 46% said “up to six months,” 26% said “up to a year,” and 20% said “more that a year.” Assume that these results are true for the 2002 population of such people. Suppose we denote the above responses by A, B, C, and D, respectively. Recently500 such people were randomly selected and asked the same question. The following table summarizes their responses.

Response	A	B	C	D
Number of people	48	242	120	90

Test at the 5% significance level whether the current distribution of response differs from the one for 2002.

58. In an At-a-Glance Communications 2002 survey, office workers were asked how long they normally took to respond to e-mail. Thirty-sex percent said “as soon as I return to my desk,” 35% said “within an hour or two,” 24% said “before the end of the business day,” and 5% said “when I can” (USA Today, May 7, 2002). Assume that these results hold true for the population of all office workers in 2002. Suppose we denote these response by A, B, C, and D, respectively. A recent random sample of 400 office workers was asked the same question and it yielded the frequency distribution shown in the following table.

Response	A	B	C	D
Frequency	128	142	116	14

Using the 1% significance level, can you conclude that the current distribution of responses differs from the 2002 distribution?

59. A survey conducted from June 21 through August 7, 2002 studied “affluent” Americans with household incomes of $75,000 or more per year (Money, Fall 2002). Part of that survey examined the relationship between the use of a financial advisor and ownership of stocks. Assuming that this portion of the survey was based on a random sample of 400 affluent Americans, the percentages given in the magazine would yield the numbers shown in the following table.

		Own Stocks	Do Not Own Stocks
Use financial	Yes	165	135
advisor?	No	43	57

At the 5% significance level, can you conclude that use of a financial advisor is related to stock ownership for all affluent Americans?

60. In a Knowledge Networks/Statistical Research 2002 survey, 8- to 17-year-olds were asked which medium was there favorite (The Reader’s Digest, November 2002). If the survey were based on random samples of 500 boys and 500 girls, the percentages given in the magazine article would have yielded the following table.

	Internet	TV	Phone	Radio	Other
Boys	190	170	60	60	20
Girls	140	85	155	85	35

Using the 1% significance level, test the null hypothesis that the distribution of media preferences is the same for boys and girls in this age group.

Linear Regression and Correlation

61. The following table gives horsepower ratings and expected gas mileage for several 2001 vehicles.

Audi A4	170 hp	22 mpg
Buick LeSabre	205	20
Chevy Blazer	190	15
Chevy Prizm	125	31
Ford Excursion	310	10
GMC Yukon	285	13
Honda Civic	127	29
Hyundai Elantr	140	25
Lexus 300	215	21
Lincoln LS	210	23
Mazda MPV	170	18
Olds Alero	140	23
Toyota Camry	194	21
VW Beetle	115	29

a. Make a scatterplot for these data.

b. Describe the direction, form, and scatter of the plot.

c. Find the correlation between horsepower and miles per gallon.

d. Write a few sentences telling what the plot says about fuel economy.

62. The following table shows the oil production of the United States from 1949 to 2000 (in millions of barrels per year).

Year	Oil	Year	Oil	Year	Oil	Year	Oil
1949	1,841,940	1962	2,676,189	1975	3,056,779	1988	2,979,123
1950	1,973,574	1963	2,752,723	1976	2,976,180	1989	2,778,773
1951	2,247,711	1964	2,786,822	1977	3,009,265	1990	2,684,687
1952	2,289,836	1965	2,848,514	1978	3,178,216	1991	2,707,039
1953	2,357,082	1966	3,027,763	1979	3,121,310	1992	2,624,632
1954	2,314,988	1967	3,215,742	1980	3,146,365	1993	2,499,033
1955	2,484,428	1968	3,329,042	1981	3,128,624	1994	2,431,476
1956	2,617,283	1969	3,371,751	1982	3,156,715	1995	2,394,268
1957	2,616,901	1970	3,517,450	1983	3,170,999	1996	2,366,017
1958	2,448,987	1971	3,453,914	1984	3,249,696	1997	2,354,831
1959	2,574,590	1972	3,455,368	1985	3,274,553	1998	2,281,919
1960	2,574,933	1973	3,360,903	1986	3,168,252	1999	2,146,732
1961	2,621,758	1974	3,202,585	1987	3,047,378	2000	2,135,062

a. Find the correlation between year and production.

b. A reporter concludes that a low correlation between year and production shows that oil production has remained steady over the 50-year period. Do you agree with this interpretation? Explain.

c. Fit a least squares regression line to oil production by year.

d. Using this regression line, predict U.S. oil production in the year 2001.

e. Does the prediction in part b look reasonable? Comment

f. Do you think the regression line is an appropriate model? Comment.

63. The following table gives the total 2002 payroll (rounded to the nearest million dollars) and the percentage of games won during the 2002 season by each of the National League baseball teams.

Team	Total Payroll	Percentage of Game Won
Arizona Diamondbacks	103	60.5
Atlanta Braves	93	63.1
Chicago Cubs	76	41.4
Cincinnati Reds	45	48.1
Colorado Rockies	57	45.1
Florida Marlins	42	48.8
Houston Astros	63	51.9
Los Angeles Dodgers	95	56.8
Milwaukee Brewers	50	34.6
Montreal Expos	39	51.2
New York Mets	95	46.6
Philadelphia Phillies	58	49.7
Pittsburgh Pirates	42	44.7
St. Louis Cardinals	75	59.9
San Diego Padres	41	40.7
San Francisco Giants	78	59.0

a. Find the least squares regression line with total payroll as an independent variable and percentage of games won as a dependent variable.

b. Give a brief interpretation of the values of the y-intercept and the slope.

c. Predict the percentage of games won for a team with a total payroll of $55 million.

64. The following table gives the total 2002 payroll (rounded to the nearest million dollars) and the percentage of games won during the 2002 season by each of the American League baseball teams.

Team	Total Payroll	Percentage of Games Won
Anaheim Angels	62	61.1
Baltimore Orioles	60	41.4
Boston Red Sox	108	57.4
Chicago White Sox	57	50.0
Cleveland Indians	79	45.7
Detroit Tigers	55	34.2
Kansas City Royals	47	38.3
Minnesota Twins	40	58.4
New York Yankees	126	64.0
Oakland A’s	40	63.6
Seattle Marines	80	57.4
Tampa Bay Devil Rays	34	34.2
Texas Rangers	106	44.4
Toronto Blue Jays	77	48.1

a. Find the least square regression line with total payroll as an independent variable and percentage of games won as a dependent variable.

b. Give a brief interpretation of the values of the y-intercept and the slope.

c. Predict the percentage of games won for a team with a total payroll of $65 million.

65. The following table gives the average hotel room rates in the United States for the years 1992-2001.

Year	Average Hotel Room Rate
1992	$59.39
1993	60.99
1994	63.35
1995	66.34
1996	70.68
1997	74.77
1998	78.24
1999	81.59
2000	85.69
2001	84.58

a. Assign a value of 0 to 1992, 1 to 1993, 2 to 1994, and so on. Call this new variable Time. Make a new table with the variables Time and Average Hotel Room Rate.

b. Construct a scatter diagram for these data. Does the scatter diagram exhibit a linear positive relationship between time and average hotel room rates?

c. Find the least squares regression line.

d. Compute the correlation coefficient r.

e. Predict the average hotel room rate for 2006. Comment on this prediction.

66. The following table shows the price of ladies diamond rings and the weight of their diamond stones. (Journal of Statistical Education, 1996)

Weight	Price	Weight	Price	Weight	Price	Weight	Price	Weight	Price	Weight	Price
.17	355	.21	483	.12	223	.17	353	.32	919	.25	655
.16	328	.15	323	.26	663	.18	438	.15	298	.35	1086
.17	350	.18	462	.25	750	.17	318	.16	339	.18	443
.18	325	.28	823	.27	720	.18	419	.16	338	.25	678
.25	642	.16	336	.18	468	.17	346	.23	595	.25	675
.16	342	.20	498	.16	345	.15	315	.23	553	.15	287
.15	322	.23	595	.17	352	.17	350	.17	345	.26	693
.19	485	.29	860	.16	332	.32	918	.33	945	.15	316

a. Construct a scatter diagram for these data.

b. Find the least squares regression line.

c. Compute the correlation coefficient r.