a. What is the point estimate of the difference between the two population means?
b. Provide a 90% confidence interval for the difference between the two population means.
c. Provide a 95% confidence interval for the difference between the two population means.
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10.2 Consider the following hypothesis test....The following results are for two independent samples taken from the two populations....
a. What is the value of the test statistic?
b. What is the p-value?
c. With α = .05, what is your hypothesis testing conclusion?
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10.3 Consider the following hypothesis test....The following results are for two independent samples taken from the two populations....
a. What is the value of the test statistic?
b. What is the p-value?
c. With α = .05, what is your hypothesis testing conclusion?
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10.4
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10.5 The average expenditure on Valentine’s Day was expected to be $100.89 (USA Today, February 13, 2006). Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 40 male consumers was $135.67, and the average expenditure in a sample survey of 30 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $35, and the standard deviation for female consumers is assumed to be $20.
a. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females?
b. At 99% confidence, what is the margin of error?
c. Develop a 99% confidence interval for the difference between the two population means.
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10.6
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10.7 During the 2003 season, Major League Baseball took steps to speed up the play of baseball games in order to maintain fan interest (CNN Headline News, September 30, 2003). The following results come from a sample of 60 games played during the summer of 2002 and a sample of 50 games played during the summer of 2003. The sample mean shows the mean duration of the games included in each sample....
a. A research hypothesis was that the steps taken during the 2003 season would reduce the population mean duration of baseball games. Formulate the null and alternative hypotheses.
b. What is the point estimate of the reduction in the mean duration of games during the 2003 season?
c. Historical data indicate a population standard deviation of 12 minutes is a reasonable assumption for both years. Conduct the hypothesis test and report the p-value. At a .05 level of significance, what is your conclusion?
d. Provide a 95% confidence interval estimate of the reduction in the mean duration of games during the 2003 season.
e. What was the percentage reduction in the mean time of baseball games during the 2003 season? Should management be pleased with the results of the statistical analysis? Discuss. Should the length of baseball games continue to be an issue in future years? Explain.
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10.8
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10.9 The following results are for independent random samples taken from two populations....
a. What is the point estimate of the difference between the two population means?
b. What is the degrees of freedom for the t distribution?
c. At 95% confidence, what is the margin of error?
d. What is the 95% confidence interval for the difference between the two population means?
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10.10 Consider the following hypothesis test....The following results are from independent samples taken from two populations....
a. What is the value of the test statistic?
b. What is the degrees of freedom for the t distribution?
c. What is the p-value?
d. At α = .05, what is your conclusion?
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10.11 Consider the following data for two independent random samples taken from two normal populations....
a. Compute the two sample means.
b. Compute the two sample standard deviations.
c. What is the point estimate of the difference between the two population means?
d. What is the 90% confidence interval estimate of the difference between the two population means?
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10.12 The U.S. Department of Transportation provides the number of miles that residents of the 75 largest metropolitan areas travel per day in a car. Suppose that for a simple random sample of 50 Buffalo residents the mean is 22.5 miles a day and the standard deviation is 8.4 miles a day, and for an independent simple random sample of 40 Boston residents the mean is 18.6 miles a day and the standard deviation is 7.4 miles a day.
a. What is the point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residents travel per day?
b. What is the 95% confidence interval for the difference between the two population means?
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10.13 FedEx and United Parcel Service (UPS) are the world’s two leading cargo carriers by volume and revenue (The Wall Street Journal, January 27, 2004). According to the Airports Council International, the Memphis International Airport (FedEx) and the Louisville International Airport (UPS) are 2 of the 10 largest cargo airports in the world. The following random samples show the tons of cargo per day handled by these airports. Data are in thousands of tons....
a. Compute the sample mean and sample standard deviation for each airport.
b. What is the point estimate of the difference between the two population means? Interpret this value in terms of the higher-volume airport and a comparison of the volume difference between the two airports.
c. Develop a 95% confidence interval of the difference between the daily population
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10.14
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10.15 Injuries to Major League Baseball players have been increasing in recent years. For the period 1992 to 2001, league expansion caused Major League Baseball rosters to increase 15%. However, the number of players being put on the disabled list due to injury increased 32% over the same period (USA Today, July 8, 2002). A research question addressed whether Major League Baseball players being put on the disabled list are on the list longer in 2001 than players put on the disabled list a decade earlier.
a. Using the population mean number of days a player is on the disabled list, formulate null and alternative hypotheses that can be used to test the research question.
b. Assume that the following data apply:
...What is the point estimate of the difference between population mean number of days on the disabled list for 2001 compared to 1992? What is the percentage increase in the number of days on the disabled list?c. Use α = .01. What is your conclusion about the number of days on the disabled list? What is the p-value?
d. Do these data suggest that Major League Baseball should be concerned about the situation?
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10.16 The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker’s parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. During 2003, the overall mean SAT verbal score was 507 (The World Almanac 2004). SAT verbal scores for independent samples of students follow. The first sample shows the SAT verbal test scores for students whose parents are college graduates with a bachelor’s degree. The second sample shows the SAT verbal test scores for students whose parents are high school graduates but do not have a college degree....
a. Formulate the hypotheses that can be used to determine whether the sample data support the hypothesis that students show a higher population mean verbal score on the SAT if their parents attained a higher level of education.
b. What is the point estimate of the difference between the means for the two populations?
c. Compute the p-value for the hypothesis test.
d. At α = .05, what is your conclusion?
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10.17 Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services. Higher ratings on the client satisfaction survey indicate better service, with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use α = .05 and test to see whether the consultant with more experience has the higher population mean service rating....
a. State the null and alternative hypotheses.
b. Compute the value of the test statistic.
c. What is the p-value?
d. What is your conclusion?
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10.18 Educational testing companies provide tutoring, classroom learning, and practice tests in an effort to help students perform better on tests such as the Scholastic Aptitude Test (SAT). The test preparation companies claim that their courses will improve SAT score performances by an average of 120 points (The Wall Street Journal, January 23, 2003). A researcher is uncertain of this claim and believes that 120 points may be an overstatement in an effort to encourage students to take the test preparation course. In an evaluation study of one test preparation service, the researcher collects SAT score data for 35 students who took the test preparation course and 48 students who did not take the course. The CD file named SAT contains the scores for this study.
a. Formulate the hypotheses that can be used to test the researcher’s belief that the improvement in SAT scores may be less than the stated average of 120 points.
b. Using α = .05, what is your conclusion?
c. What is the point estimate of the improvement in the average SAT scores provided by the test preparation course? Provide a 95% confidence interval estimate of the improvement.
d. What advice would you have for the researcher after seeing the confidence interval?
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10.19 Consider the following hypothesis test....The following data are from matched samples taken from two populations....
a. Compute the difference value for each element.
b. Compute ....
c. Compute the standard deviation sd.
d. Conduct a hypothesis test using α = .05. What is your conclusion?
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10.20 The following data are from matched samples taken from two populations....
a. Compute the difference value for each element.
b. Compute ....
c. Compute the standard deviation sd.
d. What is the point estimate of the difference between the two population means?
e. Provide a 95% confidence interval for the difference between the two population means.
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10.21 A market research firm used a sample of individuals to rate the purchase potential of a particular product before and after the individuals saw a new television commercial about the product. The purchase potential ratings were based on a 0 to 10 scale, with higher values indicating a higher purchase potential. The null hypothesis stated that the mean rating “after” would be less than or equal to the mean rating “before.” Rejection of this hypothesis would show that the commercial improved the mean purchase potential rating. Use α = .05 and the following data to test the hypothesis and comment on the value of the commercial....
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10.22 Per-share earnings data comparing the current quarter’s earnings with the previous quarter are in the CD file entitled Earnings 2005 (The Wall Street Journal, January 27, 2006). Provide a 95% confidence interval estimate of the difference between the population mean for the current quarter versus the previous quarter. Have earnings increased?
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10.23 Bank of America’s Consumer Spending Survey collected data on annual credit card charges in seven different categories of expenditures: transportation, groceries, dining out, household expenses, home furnishings, apparel, and entertainment (US Airways Attaché, December 2003). Using data from a sample of 42 credit card accounts, assume that each account was used to identify the annual credit card charges for groceries (population 1) and the annual credit card charges for dining out (population 2). Using the difference data, the sample mean difference was ..., and the sample standard deviation was sd = $1123.
a. Formulate the null and alternative hypotheses to test for no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out.
b. Use a .05 level of significance. Can you conclude that the population means differ? What is the p-value?
c. Which category, groceries or dining out, has a higher population mean annual credit card charge? What is the point estimate of the difference between the population means? What is the 95% confidence interval estimate of the difference between the population means?
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10.24 Airline travelers often choose which airport to fly from based on flight cost. Cost data (in dollars) for a sample of flights to eight cities from Dayton, Ohio, and Louisville, Kentucky, were collected to help determine which of the two airports was more costly to fly from (The Cincinnati Enquirer, February 19, 2006). A researcher argued that it is significantly more costly to fly out of Dayton than Louisville. Use the sample data to see whether they support the researcher’s argument. Use α = .05 as the level of significance....
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10.25 In recent years, a growing array of entertainment options competes for consumer time. By 2004, cable television and radio surpassed broadcast television, recorded music, and the daily newspaper to become the two entertainment media with the greatest usage (The Wall Street Journal, January 26, 2004). Researchers used a sample of 15 individuals and collected data on the hours per week spent watching cable television and hours per week spent listening to the radio....
a. Use a .05 level of significance and test for a difference between the population mean usage for cable television and radio. What is the p-value?
b. What is the sample mean number of hours per week spent watching cable television? What is the sample mean number of hours per week spent listening to radio? Which medium has the greater usage?
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10.26
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10.27 A manufacturer produces both a deluxe and a standard model of an automatic sander designed for home use. Selling prices obtained from a sample of retail outlets follow....
a. The manufacturer’s suggested retail prices for the two models show a $10 price differential. Use a .05 level of significance and test that the mean difference between the prices of the two models is $10.
b. What is the 95% confidence interval for the difference between the mean prices of the two models?
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10.28 Consider the following results for independent samples taken from two populations....
a. What is the point estimate of the difference between the two population proportions?
b. Develop a 90% confidence interval for the difference between the two population proportions.
c. Develop a 95% confidence interval for the difference between the two population proportions.
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10.29 Consider the following hypothesis test....The following results are for independent samples taken from the two populations....
a. What is the pooled estimate of p?
b. What is the p-value?
c. What is your conclusion?
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10.30 A BusinessWeek/Harris survey asked senior executives at large corporations their opinions about the economic outlook for the future. One question was, “Do you think that there will be an increase in the number of full-time employees at your company over the next 12 months?” In the current survey, 220 of 400 executives answered yes, while in a previous year survey, 192 of 400 executives had answered yes. Provide a 95% confidence interval estimate for the difference between the proportions at the two points in time. What is your interpretation of the interval estimate?
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10.31
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10.32 An American Automobile Association (AAA) study investigated the question of whether a man or a woman was more likely to stop and ask for directions (AAA, January 2006). The situation referred to in the study stated the following: “If you and your spouse are driving together and become lost, would you stop and ask for directions?” A sample representative of the data used by AAA showed 300 of 811 women said that they would stop and ask for directions, while 255 of 750 men said that they would stop and ask for directions.
a. The AAA research hypothesis was that women would be more likely to say that they would stop and ask for directions. Formulate the null and alternative hypotheses for this study.
b. What is the percentage of women who indicated that they would stop and ask for directions?
c. What is the percentage of men who indicated that they would stop and ask for directions?
d. At α = .05, test the hypothesis. What is the p-value, and what conclusion would you expect AAA to draw from this study?
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10.33
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10.34
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10.35 In a test of the quality of two television commercials, each commercial was shown in a separate test area six times over a one-week period. The following week a telephone survey was conducted to identify individuals who had seen the commercials. Those individuals were asked to state the primary message in the commercials. The following results were recorded....
a. Use α = .05 and test the hypothesis that there is no difference in the recall proportions for the two commercials.
b. Compute a 95% confidence interval for the difference between the recall proportions for the two populations.
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10.36 During the 2003 Super Bowl, Miller Lite Beer’s commercial referred to as “The Miller Lite Girls” ranked among the top three most effective advertisements aired during the Super Bowl (USA Today, December 29, 2003). The survey of advertising effectiveness, conducted by USA Today’s Ad Track poll, reported separate samples by respondent age group to learn about how the Super Bowl advertisement appealed to different age groups. The following sample data apply to the “The Miller Lite Girls” commercial....
a. Formulate a hypothesis test that can be used to determine whether the population proportions for the two age groups differ.
b. What is the point estimate of the difference between the two population proportions?
c. Conduct the hypothesis test and report the p-value. At α = .05, what is your conclusion?
d. Discuss the appeal of the advertisements to the younger and the older age groups. Would the Miller Lite organization find the results of the USA Today Ad Track poll encouraging? Explain.
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10.37 A 2003 New York Times/CBS News poll sampled 523 adults who were planning a vacation during the next six months and found that 141 were expecting to travel by airplane (New York Times News Service, March 2, 2003). A similar survey question in a May 1993 New York Times/CBS News poll found that of 477 adults who were planning a vacation in the next six months, 81 were expecting to travel by airplane.
a. State the hypotheses that can be used to determine whether a significant change occurred in the population proportion planning to travel by airplane over the 10-year period.
b. What is the sample proportion expecting to travel by airplane in 2003? In 1993?
c. Use α = .01 and test for a significant difference. What is your conclusion?
d. Discuss reasons that might provide an explanation for this conclusion.
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10.38 Safegate Foods, Inc., is redesigning the checkout lanes in its supermarkets throughout the country and is considering two designs. Tests on customer checkout times conducted at two stores where the two new systems have been installed result in the following summary of the data....Test at the .05 level of significance to determine whether the population mean checkout times of the two systems differ. Which system is preferred?
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10.39
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10.40 Mutual funds are classified as load or no-load funds. Load funds require an investor to pay an initial fee based on a percentage of the amount invested in the fund. The no-load funds do not require this initial fee. Some financial advisors argue that the load mutual funds may be worth the extra fee because these funds provide a higher mean rate of return than the no-load mutual funds. A sample of 30 load mutual funds and a sample of 30 no-load mutual funds were selected. Data were collected on the annual return for the funds over a five-year period. The data are contained in the data set Mutual. The data for the first five load and first five no-load mutual funds are as follows....
a. Formulate H0 and Ha such that rejection of H0 leads to the conclusion that the load mutual funds have a higher mean annual return over the five-year period.
b. Use the 60 mutual funds in the data set Mutual to conduct the hypothesis test. What is the p-value? At α = .05, what is your conclusion?
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10.41 The National Association of Home Builders provided data on the cost of the most popular home remodeling projects. Sample data on cost in thousands of dollars for two types of remodeling projects are as follows....
a. Develop a point estimate of the difference between the population mean remodelling costs for the two types of projects.
b. Develop a 90% confidence interval for the difference between the two population means.
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10.42
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10.43 Jupiter Media used a survey to determine how people use their free time. Watching television was the most popular activity selected by both men and women (The Wall Street Journal, January 26, 2004). The proportion of men and the proportion of women who selected watching television as their most popular leisure time activity can be estimated from the following sample data....
a. State the hypotheses that can be used to test for a difference between the proportion for the population of men and the proportion for the population of women who selected watching television as their most popular leisure time activity.
b. What is the sample proportion of men who selected watching television as their most popular leisure time activity? What is the sample proportion of women?
c. Conduct the hypothesis test and compute the p-value. At a .05 level of significance, what is your conclusion?
d. What is the margin of error and 95% confidence interval estimate of the difference between the population proportions?
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10.44
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10.45 Medical tests were conducted to learn about drug-resistant tuberculosis. Of 142 cases tested in New Jersey, 9 were found to be drug-resistant. Of 268 cases tested in Texas, 5 were found to be drug-resistant. Do these data suggest a statistically significant difference between the proportions of drug-resistant cases in the two states? Use a .02 level of significance. What is the p-value, and what is your conclusion?
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10.46
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10.47
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