Statistics For Business & Economics

David Ray Anderson, Jeffrey D. Camm, James J. Cochran, Dennis J. Sweeney, Thomas Arthur Williams

Chapter 10

Inference about Means and Proportions with Two Populations - all with Video Answers

Educators

Chapter Questions

Problem 1

The following results come from two independent random samples taken of two populations.
$\begin{array}{ll}\text { Sample 1 } & \text { Sample 2 } \\ n_1=50 & n_2=35 \\ \vec{x}_1=13.6 & \vec{x}_2=11.6 \\ \sigma_1=2.2 & \sigma_2=3.0\end{array}$
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.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 2

Consider the following hypothesis test.
$$
\begin{aligned}
& H_6: \mu_1-\mu_2 \leq 0 \\
& H_2: \mu_1-\mu_2>0
\end{aligned}
$$
The following results are for two independent samples taken from the two populations.
$\begin{array}{ll}\text { Sample 1 } & \text { Sample 2 } \\ n_1=40 & n_2=50 \\ \bar{x}_1=25.2 & \bar{x}_2=22.8 \\ \sigma_1=5.2 & \sigma_2=6.0\end{array}$
a. What is the value of the test statistic?
b. What is the p-value?
c. With $\alpha=.05$, what is your hypothesis testing conclusion?

Kari Hasz

Numerade Educator

Problem 3

Consider the following hypothesis test.
$$
\begin{aligned}
& H_e: \mu_1-\mu_2=0 \\
& H_2: \mu_1-\mu_2 \neq 0
\end{aligned}
$$
The following results are for two independent samples taken from the two populations.
$$
\begin{array}{ll}
\text { Sample 1 } & \text { Sample 2 } \\
n_1=80 & n_2=70 \\
\bar{x}_1=104 & \bar{x}_3=106 \\
\sigma_1=8.4 & \sigma_2=7.6
\end{array}
$$
a. What is the value of the test statistic?
b. What is the $p$-value?
c. With $\alpha=.05$, what is your hypothesis testing conclusion?

Kari Hasz

Numerade Educator

Problem 4

4. Conde 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 . 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?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 5

The USA Today reports that the average expenditure on Valentine's Day is $$\$100.89$$. 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.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 6

Suppose that you are responsible for making arrangements for a business convention and that 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 file 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 Attanta 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?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 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.
$\begin{array}{ll}\text { Target } & \text { Walmart } \\ n_1=25 & n_2=30 \\ \vec{x}_1=79 & \vec{x}_2=71\end{array}$
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.

Kari Hasz

Numerade Educator

Problem 8

Will improving customer service result in higher stock prices for the companies providing the better service? "When a company's satisfaction score has improved over the prior year's results and is above the national average (75.7). studies show its shares have a good chance of outperforming the broad stock market in the long run." The following satisfaction scores of three companies for the 4 th quarters of two previous years were obtained from the American Customer Satisfaction Index. Assume that the scores are based on a poll of 60 customers from each company. Because the polling has been done for several years, the standard deviation can be assumed to equal 6 points in each case.
$$
\begin{array}{lcc}
\text { Company } & \text { Year 1 } & \text { Year 2 } \\
\text { Rite Aid } & 73 & 76 \\
\text { Expedia } & 75 & 77 \\
\text { J.C. Penney } & 77 & 78
\end{array}
$$
a. For Rite Aid, is the increase in the satisfaction score from year 1 to year 2 statistically significant? Use $\alpha=.05$. What can you conclude?
b. Can you conclude that the year 2 score for Rite Aid is above the national average of 75.7 ? Use $\alpha=05$
c. For Expedia, is the increase from year 1 to year 2 statistically significant? Use $\alpha=.05$.
d. When conducting a hypothesis test with the values given for the standard deviation, sample size, and $\alpha$, how large must the increase from year 1 to year 2 be for it to be statistically significant?
e. Use the result of part (d) to state whether the increase for J.C. Penney from year I to year 2 is statistically significant.

Kari Hasz

Numerade Educator

Problem 9

The following results are for independent random samples taken from two populations.
$\begin{array}{ll}\text { Sample 1 } & \text { Sample 2 } \\ n_1=20 & n_2=30 \\ \bar{x}_1=22.5 & \bar{x}_2=20.1 \\ s_1=2.5 & s_2=4.8\end{array}$
a. What is the point estimate of the difference between the two population means?
b. What is the degrees of freedom for the $r$ distribution?
c. At $95 \%$ confidence, what is the margin of crror?
d. What is the $95 \%$ confidence interval for the difference between the two population means?

Kari Hasz

Numerade Educator

Problem 10

Consider the following hypothesis test.
$$
\begin{aligned}
& H_0: \mu_1-\mu_2=0 \\
& H_a: \mu_1-\mu_2 \neq 0
\end{aligned}
$$
The following results are from independent samples taken from two populations.
$$
\begin{array}{ll}
\text { Sample 1 } & \text { Sample 2 } \\
n_1=35 & n_2=40 \\
\vec{x}_1=13.6 & \vec{x}_2=10.1 \\
s_1=5.2 & s_2=8.5
\end{array}
$$
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 $\alpha=.05$, what is your conclusion?

Kari Hasz

Numerade Educator

Problem 11

Consider the following data for two independent random samples taken from two nomal populations.
$$
\begin{array}{l|rrrrrr}
\text { Sample 1 } & 10 & 7 & 13 & 7 & 9 & 8 \\
\hline \text { Sample 2 } & 8 & 7 & 8 & 4 & 6 & 9
\end{array}
$$
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?

Alexander Cheng

Alexander Cheng

Numerade Educator

Problem 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?

Srikar Katta

Numerade Educator

Problem 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 collegeage 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.
Private Colleges
$$
\begin{array}{lllll}
52.8 & 43.2 & 45.0 & 33.3 & 44.0 \\
30.6 & 45.8 & 37.8 & 50.5 & 42.0
\end{array}
$$
Private Colleges
$$
\begin{array}{llllll}
20.3 & 22.0 & 28.2 & 15.6 & 24.1 & 28.5 \\
22.8 & 25.8 & 18.5 & 25.6 & 14.4 & 21.8
\end{array}
$$
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 public colleges.

Kari Hasz

Numerade Educator

Problem 14

Are nursing salaries in Tampa, Florida, lower than those in Dallas, Texas? As reported by the Tampa Tribune, salary data show staff nurses in Tampa earn less than staff nurses in Dallas. 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 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 $\alpha=.05$.
b. What is the value of the test statistic?
c. What is the p-value?
d. What is your conclusion?

Srikar Katta

Numerade Educator

Problem 15

Commercial real estate prices and rental rates suffered substantial declines in 2008 and 2009 (Newsweek, July 27, 2009). These declines were particularly severe in Asia; annual lease rates in Tokyo, Hong Kong, and Singapore declined by $40 \%$ or more. Even with such large declines, annual lease rates in Asia were still higher than those in many cities in Europe. Annual lease rates for a sample of 30 commercial properties in Hong Kong showed a mean of $$\$1,114$$ per square meter with a standard deviation of $$\$230$$.
Annual lease rates for a sample of 40 commercial properties in Paris showed a mean lease rate of $$\$ 989$$ per square meter with a standard deviation of $$\$ 195$$.
a. On the basis of the sample results, can we conclude that the mean annual lease rate is higher in Hong Kong than in Paris? Develop appropriate null and alternative hypotheses.
b. Use $\alpha=.01$. What is your conclusion?

Nick Johnson

Numerade Educator

Problem 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 $\alpha=.05$, what is your conclusion?

Sheryl Ezze

Numerade Educator

Problem 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 $\alpha=.05$ and test to see whether the consultant with more experience has the higher population mean service rating.

Kari Hasz

Numerade Educator

Problem 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 ontime 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 file 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?

Kari Hasz

Numerade Educator

Problem 19

Consider the following hypothesis test.
$$
\begin{aligned}
& H_0: \mu_d \leq 0 \\
& H_a: \mu_d>0
\end{aligned}
$$
The following data are from matched samples taken from two populations.
a. Compute the difference value for each element.
b. Compute $\bar{d}$.
c. Compute the standard deviation $s_d$.
d. Conduct a hypothesis test using $\alpha=.05$. What is your conclusion?

Kari Hasz

Numerade Educator

Problem 20

The following data are from matched samples taken from two populations.
a. Compute the difference value for each element.
b. Compute $\vec{d}$.
c. Compute the standard deviation $s_d$.
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.

Kari Hasz

Numerade Educator

Problem 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 $\alpha=.05$ and the following data to test the hypothesis and comment on the value of the commercial.

Sheryl Ezze

Numerade Educator

Problem 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 Ist quarter of 2012 (The Wall Sireet Joumal, 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 file entitled StockPrices to answer the following.
a. Let $d_i$ denote the change in price per share for company $i$ where $d_i=1$ st 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.

Dominador Tan

Numerade Educator

Problem 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 $$\bar{d}=\$ 850$$, and the sample standard deviation was $$s_d=\$ 1123$$.
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?

Kari Hasz

Numerade Educator

Problem 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?

Sheryl Ezze

Numerade Educator

Problem 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?

Sheryl Ezze

Numerade Educator

Problem 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. 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 $\alpha=.10$ 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.

Sheryl Ezze

Numerade Educator

Problem 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?

Sheryl Ezze

Numerade Educator

Problem 28

Consider the following results for independent samples taken from two populations.
$\begin{array}{ll}\text { Sample 1 } & \text { Sample 2 } \\ n_1=400 & n_2=300 \\ \bar{p}_1=.48 & \bar{p}_2=.36\end{array}$
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.

Rashmi Sinha

Numerade Educator

Problem 29

Consider the hypothesis test
$$
\begin{aligned}
& H_0: p_1-p_2 \leq 0 \\
& H_3: p_1-p_2>0
\end{aligned}
$$
The following results are for independent samples taken from the two populations.
a. What is the $p$-value?
b. With $\alpha=.05$, what is your hypothesis testing conclusion?

Sheryl Ezze

Numerade Educator

Problem 30

A Businessweed/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?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 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.
$$
\begin{array}{lcc}
& \text { Women } & \text { Men } \\
\text { Sample } & 150 & 170 \\
\text { Trust Recommendations Made on Pinterest } & 117 & 102
\end{array}
$$
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.

Sheryl Ezze

Numerade Educator

Problem 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 Chnonicle 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.
$$
\begin{array}{lcc}
& \text { Tuna } & \text { Mahi Mahi } \\
\text { Sample } & 220 & 160 \\
\text { Mislabeled } & 99 & 56
\end{array}
$$
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.

Sheryl Ezze

Numerade Educator

Problem 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 $\alpha=.05$, test the political analysts" hypothesis. What is the $p$-value, and what conclusion do you draw from your results?

Sheryl Ezze

Numerade Educator

Problem 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.
$$
\begin{array}{lcc}
& 2005 & 2012 \\
\text { Wells Drilled } & 119 & 162 \\
\text { Dry Wells } & 24 & 18
\end{array}
$$
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 $\alpha=.05$, what conclusion do you draw from your results?

Sheryl Ezze

Numerade Educator

Problem 35

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?

Sheryl Ezze

Numerade Educator

Problem 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.
$$
\begin{array}{lcc}
& \text { Current Year } & \text { Previous Year } \\
\text { Occupied Rooms } & 1470 & 1458 \\
\text { Total Rooms } & 1750 & 1800
\end{array}
$$
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 ycar?
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?

Sheryl Ezze

Numerade Educator

Problem 37

The Adecco Workplace Insights Survey sampled men and women workers and asked if they expected to get a raise or promotion this year (U/SA 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 in that you can conclude a greater proportion of men are expecting 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?

Sheryl Ezze

Numerade Educator

Problem 38

Safegate Foods, Inc., is redesigning the checkout lanes in its supermarkets throughout the country and is considering two dessigns. 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?

Sheryl Ezze

Numerade Educator

Problem 39

Home values tend to increase over time under normal conditions, but the recession of 2008 and 2009 has reportedly caused the sales 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?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 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 $H_0$ and $H_a$ such that rejection of $H_0$ leads to the conclusion that the load mutual funds have a higher mean annual retum 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 $\alpha=.05$, what is your conclusion?

Srikar Katta

Numerade Educator

Problem 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.

Sheryl Ezze

Numerade Educator

Problem 42

In Bom Together-Reared Apart: The Landwark Minnesota Twin Study (2012), Nancy Segal discusses the efforts of research psychologists at the University of Minnesota to understand similarities and differences between twins by studying sets of twins who were raised separately. Below are critical reading SAT scores for several pairs of identical twins (twins who share all of their genes), one of whom was raised in a family with no other children (no siblings) and one of whom was raised in a family with other children (with siblings).
a. What is the mean difference between the critical reading SAT scores for the twins raised with no siblings and the twins raised with siblings?
b. Provide a $90 \%$ confidence interval estimate of the mean difference between the critical reading SAT scores for the twins raised with no siblings and the twins raised with siblings.
c. Conduct a hypothesis test of equality of the critical reading SAT scores for the twins raised with no siblings and the twins raised with siblings at $\alpha=.01$. What is your conclusion?

Sheryl Ezze

Numerade Educator

Problem 43

Country Financial, a financial services company, uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time (USA Today, April 4, 2012). In February 2012, a sample of 1000 adults showed 410 indicating that their financial security was more than fair. In February 2010, a sample of 900 adults showed 315 indicating that their financial security was more than fair.
a. State the hypotheses that can be used to test for a significant difference between the population proportions for the two years.
b. What is the sample proportion indicating that their financial security was more than fair in 2012 ? In 2010 ?
c. Conduct the hypothesis test and compute the $p$-value. At a .05 level of significance, what is your conclusion?
d. What is the $95 \%$ confidence interval estimate of the difference between the two population proportions?

Sheryl Ezze

Numerade Educator

Problem 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 threeyear period.
a. Use $\alpha=.05$. 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.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 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?

Rashmi Sinha

Numerade Educator

Problem 46

Vacation occupancy rates were expected to be up during March 2008 in Myrtle Beach, South Carolina (The Sun News, February 29, 2008). Data in the file Occupancy will allow you to replicate the findings presented in the newspaper. The data show units rented and not rented for a random sample of vacation properties during the first week of March 2007 and March 2008.
a. Estimate the proportion of units rented during the first week of March 2007 and the first week of March 2008.
b. Provide a $95 \%$ confidence interval for the difference in proportions.
c. On the basis of your findings, does it appear March rental rates for 2008 will be up from those a year earlier?

Srikar Katta

Numerade Educator

Problem 47

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 oneyear period? Do you think area officials would be pleased with the results?

Sheryl Ezze

Numerade Educator