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 Condé Nast Traveler conducts an annual survey in which readers rate their favorite cruise ship. All ships are rated on a 100-point scale, with higher values indicating better service. A sample of 37 ships that carry fewer than 500 passengers resulted in an average rating of 85.36, and a sample of 44 ships that carry 500 or more passengers provided an average rating of 81.40 (Condé Nast Traveler, February 2008). Assume that the population standard deviation is 4.55 for ships that carry fewer than 500 passengers and 3.97 for ships that carry 500 or more passengers.
a. What is the point estimate of the difference between the population mean rating for ships that carry fewer than 500 passengers and the population mean rating for ships that carry 500 or more passengers?
b. At 95% confidence, what is the margin of error?
c. What is a 95% confidence interval estimate of the difference between the population mean ratings for the two sizes of ships?
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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 Suppose that you are responsible for making arrangements for a business convention. Because of budget cuts due to the recent recession, you have been charged with choosing a city for the convention that has the least expensive hotel rooms. You have narrowed your choices to Atlanta and Houston. The WEBfile named Hotel contains samples of prices for rooms in Atlanta and Houston that are consistent with the results reported by Smith Travel Research (SmartMoney, March 2009). Because considerable historical data on the prices of rooms in both cities are available, the population standard deviations for the prices can be assumed to be $20 in Atlanta and $25 in Houston. Based on the sample data, can you conclude that the mean price of a hotel room in Atlanta is lower than one in Houston?
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10.7 Consumer Reports uses a survey of readers to obtain customer satisfaction ratings for the nation’s largest retailers (Consumer Reports, March 2012). Each survey respondent is asked to rate a specified retailer in terms of six factors: quality of products, selection, value, checkout efficiency, service, and store layout. An overall satisfaction score summarizes the rating for each respondent with 100 meaning the respondent is completely satisfied in terms of all six factors. Sample data representative of independent samples of Target and Walmart customers are shown below....
a. Formulate the null and alternative hypotheses to test whether there is a difference between the population mean customer satisfaction scores for the two retailers.
b. Assume that experience with the Consumer Reports satisfaction rating scale indicates that a population standard deviation of 12 is a reasonable assumption for both retailers. Conduct the hypothesis test and report the p-value. At a .05 level of significance what is your conclusion?
c. Which retailer, if either, appears to have the greater customer satisfaction? Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers.
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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 a = .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 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 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 The average annual cost (including tuition, room, board, books, and fees) to attend a public college takes nearly a third of the annual income of a typical family with college-age children (Money, April 2012). At private colleges, the average annual cost is equal to about 60% of the typical family’s income. The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars....
a. Compute the sample mean and sample standard deviation for private and public colleges.
b. What is the point estimate of the difference between the two population means? Interpret this value in terms of the annual cost of attending private and public colleges.
c. Develop a 95% confidence interval of the difference between the mean annual cost of attending private and pubic colleges.
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10.14 Are nursing salaries in Tampa, Florida, lower than those in Dallas, Texas? Salary data show staff nurses in Tampa earn less than staff nurses in Dallas (The Tampa Tribune, January 15, 2007). Suppose that in a follow-up study of 40 staff nurses in Tampa and 50 staff nurses in Dallas you obtain the following results....
a. Formulate a hypothesis so that, if the null hypothesis is rejected, we can conclude that salaries for staff nurses in Tampa are significantly lower than for those in Dallas. Use α = .05.
b. What is the value of the test statistic?
c. What is the p-value?d. What is your conclusion?
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10.15
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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. The overall mean SAT math score was 514 (College Board website, January 8, 2012). SAT math scores for independent samples of students follow. The first sample shows the SAT math test scores for students whose parents are college graduates with a bachelor’s degree. The second sample shows the SAT math 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 math 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 Researchers at Purdue University and Wichita State University found that airlines are doing a better job of getting passengers to their destinations on time (Associated Press, April 2, 2012). AirTran Airways and Southwest Airlines were among the leaders in on-time arrivals, with both having 88% of their flights arriving on time. But for the 12% of flights that were delayed, how many minutes were these flights late? Sample data showing the number of minutes that delayed flights were late are provided in the WEBfile named AirDelay. Data are shown for both airlines.
a. Formulate the hypotheses that can be used to test for a difference between the population mean minutes late for delayed flights by these two airlines.
b. What is the sample mean number of minutes late for delayed flights for each of these two airlines?
c. Using a .05 level of significance, what is the p-value and what is your conclusion?
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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 The price per share of stock for a sample of 25 companies was recorded at the beginning of 2012 and then again at the end of the 1st quarter of 2012 (The Wall Street Journal, April 2, 2012). How stocks perform during the 1st quarter is an indicator of what is ahead for the stock market and the economy. Use the sample data in the WEBfile named StockPrices to answer the following.
a. Let di denote the change in price per share for company i where di= 1st quarter of 2012 price per share minus the beginning of 2012 price per share. Use the sample mean of these values to estimate the dollar amount a share of stock has changed during the 1st quarter.
b. What is the 95% confidence interval estimate of the population mean change in the price per share of stock during the first quarter? Interpret this result.
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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. 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 The Global Business Travel Association reported the domestic airfare for business travel for the current year and the previous year (Inc. magazine, February 2012). Below is a sample of 12 flights with their domestic airfares shown for both years....
a. Formulate the hypotheses and test for a significant increase in the mean domestic airfare for business travel for the one-year period. What is the p-value? Using a .05 level of significance, what is your conclusion?
b. What is the sample mean domestic airfare for business travel for each year?
c. What is the percentage change in the airfare for the one-year period?
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10.25 The College Board SAT college entrance exam consists of three parts: math, writing, and critical reading (The World Almanac, 2012). Sample data showing the math and writing scores for a sample of 12 students who took the SAT follow....
a. Use a .05 level of significance and test for a difference between the population mean for the math scores and the population mean for the writing scores. What is the p-value and what is your conclusion?
b. What is the point estimate of the difference between the mean scores for the two tests? What are the estimates of the population mean scores for the two tests? Which test reports the higher mean score?
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10.26 Scores in the first and fourth (final) rounds for a sample of 20 golfers who competed in PGA tournaments are shown in the following table (Golfweek, February 14, 2009, and February 28, 2009). Suppose you would like to determine if the mean score for the first round of a PGA Tour event is significantly different than the mean score for the fourth and final round. Does the pressure of playing in the final round cause scores to go up? Or does the increased player concentration cause scores to come down?...
a. Use α = .10 to test for a statistically significantly difference between the population means for first- and fourth-round scores. What is the p-value? What is your conclusion?
b. What is the point estimate of the difference between the two population means? For which round is the population mean score lower?
c. What is the margin of error for a 90% confidence interval estimate for the difference between the population means? Could this confidence interval have been used to test the hypothesis in part (a)? Explain.
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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
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10.30 A Bloomberg 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 Forbes reports that women trust recommendations from Pinterest more than recommendations from any other social network platform (Forbes website, April 10, 2012). But does trust in Pinterest differ by gender? The following sample data show the number of women and men who stated in a recent sample that they trust recommendations made on Pinterest....
a. What is the point estimate of the proportion of women who trust recommendations made on Pinterest?
b. What is the point estimate of the proportion of men who trust recommendations made on Pinterest?
c. Provide a 95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on Pinterest.
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10.32 Researchers with Oceana, a group dedicated to preserving the ocean ecosystem, reported finding that 33% of fish sold in retail outlets, grocery stores, and sushi bars throughout the United States had been mislabeled (San Francisco Chronicle website, February 21, 2013). Does this mislabeling differ for different species of fish? The following data show the number labeled incorrectly for samples of tuna and mahi mahi....
a. What is the point estimate of the proportion of tuna that is mislabeled?
b. What is the point estimate of the proportion of mahi mahi that is mislabeled?
c. Provide a 95% confidence interval estimate of the difference between the proportion of tuna and mahi mahi that is mislabeled.
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10.33 Minnesota had the highest turnout rate of any state for the 2012 presidential election (United States Election Project website, February 9, 2013). Political analysts wonder if turnout in rural Minnesota was higher than turnout in the urban areas of the state. A sample shows that 663 of 884 registered voters from rural Minnesota voted in the 2012 presidential election, while 414 out of 575 registered voters from urban Minnesota voted.
a. Formulate the null and alternative hypotheses that can be used to test whether registered voters in rural Minnesota were more likely than registered voters in urban Minnesota to vote in the 2012 presidential election.
b. What is the proportion of sampled registered voters in rural Minnesota that voted in the 2012 presidential election?
c. What is the proportion of sampled registered voters in urban Minnesota that voted in the 2012 presidential election?
d. At α = .05, test the political analysts’ hypothesis. What is the p-value, and what conclusion do you draw from your results?
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10.34 Oil wells are expensive to drill, and dry wells are a great concern to oil exploration companies. The domestic oil and natural gas producer Aegis Oil, LLC describes on its website how improvements in technologies such as three-dimensional seismic imaging have dramatically reduced the number of dry (nonproducing) wells it and other oil exploration companies drill. The following sample data for wells drilled in 2005 and 2012 show the number of dry wells that were drilled in each year....
a. Formulate the null and alternative hypotheses that can be used to test whether the wells drilled in 2005 were more likely to be dry than wells drilled in 2012.
b. What is the point estimate of the proportion of wells drilled in 2005 that were dry?
c. What is the point estimate of the proportion of wells drilled in 2012 that were dry?
d. What is the p-value of your hypothesis test? At α = .05, what conclusion do you draw from your results?
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10.35
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10.36 Winter visitors are extremely important to the economy of Southwest Florida. Hotel occupancy is an often-reported measure of visitor volume and visitor activity (Naples Daily News, March 22, 2012). Hotel occupancy data for February in two consecutive years are as follows....
a. Formulate the hypothesis test that can be used to determine if there has been an increase in the proportion of rooms occupied over the one-year period.
b. What is the estimated proportion of hotel rooms occupied each year?
c. Using a .05 level of significance, what is your hypothesis test conclusion? What is the p-value?
d. What is the 95% confidence interval estimate of the change in occupancy for the one-year period? Do you think area officials would be pleased with the results?
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10.37 The Adecco Workplace Insights Survey sampled men and women workers and asked if they expected to get a raise or promotion this year (USA Today, February 16, 2012). Suppose the survey sampled 200 men and 200 women. If 104 of the men replied Yes and 74 of the women replied Yes, are the results statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year?
a. State the hypothesis test in terms of the population proportion of men and the population proportion of women.
b. What is the sample proportion for men? For women?
c. Use a .01 level of significance. What is the p-value and what is your conclusion?
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10.38 Home values tend to increase over time under normal conditions, but the recession of 2008 and 2009 has reportedly caused the resale price of existing homes to fall nationwide (BusinessWeek, March 9, 2009). You would like to see if the data support this conclusion. The file HomePrices contains data on 30 existing home sales in 2006 and 40 existing home sales in 2009.
a. Provide a point estimate of the difference between the population mean prices for the two years.
b. Develop a 99% confidence interval estimate of the difference between the resale prices of houses in 2006 and 2009.
c. Would you feel justified in concluding that resale prices of existing homes have declined from 2006 to 2009? Why or why not?
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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 • = .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 remodeling 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
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10.44 A large automobile insurance company selected samples of single and married male policyholders and recorded the number who made an insurance claim over the preceding three-year period....
a. Use α = .05. Test to determine whether the claim rates differ between single and married male policyholders.
b. Provide a 95% confidence interval for the difference between the proportions for the two populations.
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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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