Essentials of Modern Business Statistics

David R. Anderson, Dennis J. Sweeney,Thomas A. Williams

Chapter 10

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

Educators

Chapter Questions

Problem 1

1. The following results come from two independent random samples taken of two populations.
Sample $1 \quad$ Sample 2
$$
\begin{array}{ll}
n_{1}=50 & n_{2}=35 \\
\bar{x}_{1}=13.6 & \bar{x}_{2}=11.6 \\
\sigma_{1}=2.2 & \sigma_{2}=3.0
\end{array}
$$
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.

Kari Hasz

Kari Hasz

Numerade Educator

Problem 2

Consider the following hypothesis test.
$$
\begin{array}{l}
H_{0}: \mu_{1}-\mu_{2} \leq 0 \\
H_{\mathrm{a}}: \mu_{1}-\mu_{2}>0
\end{array}
$$
The following results are for two independent samples taken from the two populations.
Sample $1 \quad$ Sample 2
$$
\begin{array}{ll}
n_{1}=40 & n_{2}=50 \\
\bar{x}_{1}=25.2 & \bar{x}_{2}=22.8 \\
\sigma_{1}=5.2 & \sigma_{2}=6.0
\end{array}
$$
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.
$$
\begin{array}{l}
H_{0}: \mu_{1}-\mu_{2}=0 \\
H_{\mathrm{a}}: \mu_{1}-\mu_{2} \neq 0
\end{array}
$$
The following results are for two independent samples taken from the two populations.
Sample $1 \quad$ Sample 2
$$
\begin{array}{ll}
n_{1}=80 & n_{2}=70 \\
\bar{x}_{1}=104 & \bar{x}_{2}=106 \\
\sigma_{1}=8.4 & \sigma_{2}=7.6
\end{array}
$$
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

Cruise Ship Ratings. 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 $81.40 .$ 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?

Kari Hasz

Numerade Educator

Problem 5

Valentine's Day Expenditures. 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.

Nick Johnson

Numerade Educator

Problem 6

Hotel Price Comparison. 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 Hotel contains samples of prices for rooms in Atlanta and Houston that are consistent with a SmartMoney survey conducted by Smith Travel Research. 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?

Kari Hasz

Numerade Educator

Problem 7

Supermarket Customer Satisfaction. Consumer Reports uses a survey of readers to obtain customer satisfaction ratings for the nation's largest supermarkets (Consumer Reports website). Each survey respondent is asked to rate a specified supermarket based on a variety of factors such as 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 factors. Sample data representative of independent samples of Publix and Trader Joe's customers are shown below.
Publix $\quad$ Trader Joe's
$$
\begin{array}{ll}
n_{1}=250 & n_{2}=300 \\
\bar{x}_{1}=86 & \bar{x}_{2}=85
\end{array}
$$
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

Increases in Customer Satisfaction. 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 fourth 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.
$\begin{array}{lcc}\text { Company } & \text { Year } 1 \text { Score } & \text { Year } 2 \text { Score } \\ \text { Rite Aid } & 73 & 76 \\ \text { Expedia } & 75 & 77 \\ \text { J.C. Penney } & 77 & 78\end{array}$
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 1 to Year 2 is statistically significant.

Kari Hasz

Numerade Educator

Problem 9

The following results are for independent random samples taken from two populations.
Sample 1 Sample 2
$\begin{array}{ll}n_{1}=20 & n_{2}=30 \\ \bar{x}_{1}=22.5 & \bar{x}_{2}=20.1 \\ s_{1}=2.5 & s_{2}=4.8\end{array}$
a. What is the point estimate of the difference between the two population means?
b. What is the degrees of freedom for the $t$ 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?

Kari Hasz

Numerade Educator

Problem 10

Consider the following hypothesis test.
$$
\begin{array}{l}
H_{0}: \mu_{1}-\mu_{2}=0 \\
H_{a}: \mu_{1}-\mu_{2} \neq 0
\end{array}
$$
The following results are from independent samples taken from two populations.
$$
\begin{array}{ll}
\text { Sample } 1 & \text { Sample } 2 \\
n_{1}=35 & n_{2}=40 \\
\bar{x}_{1}=13.6 & \bar{x}_{2}=10.1 \\
s_{1}=5.2 & s_{2}=8.5
\end{array}
$$
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 normal populations.
\begin{tabular}{l|rrrrrr}
Sample 1 & 10 & 7 & 13 & 7 & 9 & 8 \\
\hline Sample 2 & 8 & 7 & 8 & 4 & 6 & 9
\end{tabular}
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?

Kari Hasz

Numerade Educator

Problem 11

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

Kari Hasz

Numerade Educator

Problem 12

Miles Driven Per Day. 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?

Kari Hasz

Numerade Educator

Problem 13

Annual cost of College. The increasing annual cost (including tuition, room, board, books, and fees) to attend college has been widely discussed in many publications including Money magazine. The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars.
$$
\begin{aligned}
&\text { Private Colleges }\\
&\begin{array}{lllll}
52.8 & 43.2 & 45.0 & 33.3 & 44.0 \\
30.6 & 45.8 & 37.8 & 50.5 & 42.0
\end{array}
\end{aligned}
$$
$$
\begin{aligned}
&\text { Public Colleges }\\
&\begin{array}{llllll}
20.3 & 22.0 & 28.2 & 15.6 & 24.1 & 28.5 \\
22.8 & 25.8 & 18.5 & 25.6 & 14.4 & 21.8
\end{array}
\end{aligned}
$$
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

Salaries of Recent College Graduates. The Tippie College of Business obtained the following results on the salaries of a recent graduating class: Finance Majors
$$
\begin{array}{l}
n_{1}=110 \\
\bar{x}_{1}=\$ 48,537 \\
s_{1}=\$ 18,000
\end{array}
$$ Business Analytics Majors
$$
\begin{array}{l}
n_{2}=30 \\
\bar{x}_{2}=\$ 55,317 \\
s_{2}=\$ 10,000
\end{array}
$$
a. Formulate a hypothesis so that, if the null hypothesis is rejected, we can conclude that salaries for Finance majors are significantly lower than the salaries of Business Analytics majors. Use $\alpha=.05$.
b. What is the value of the test statistic?
c. What is the $p$ -value?
d. What is your conclusion?

Sheryl Ezze

Numerade Educator

Problem 15

Hotel Prices. Hotel room pricing changes over time, but is there a difference between Europe hotel prices and U.S. hotel prices? The file IntHotels contains changes in the hotel prices for 47 major European cities and 53 major U.S. cities.
a. On the basis of the sample results, can we conclude that the mean change in hotel rates in Europe and the United States are different? Develop appropriate null and alternative hypotheses.
b. Use $\alpha=.01 .$ What is your conclusion?

Kari Hasz

Numerade Educator

Problem 16

Effect of Parents' Education on Student SAT Scores. 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 $514 .$ 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

Comparing Financial Consultant Ratings. 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 $\mathrm{B}$ 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.
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?

Kari Hasz

Numerade Educator

Problem 18

Comparing Length of Flight Delays. The success of an airline depends heavily on its ability to provide a pleasant customer experience. One dimension of customer service on which airlines compete is on-time arrival. The file LateFlights contains a sample of data from delayed flights showing the number of minutes each delayed flight was late for two different airlines, Delta and Southwest.
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.
$$
\begin{array}{l}
H_{0}: \mu_{d} \leq 0 \\
H_{\mathrm{a}}: \mu_{d}>0
\end{array}
$$
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 $\bar{d}$.
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

Television Commercials and Product Purchase Potential. 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.

Kari Hasz

Numerade Educator

Problem 22

First Quarter Stock Market Performance. The price per share of stock for a sample of 25 companies was recorded at the beginning of the first financial quarter and then again at the end of the first financial quarter. How stocks perform during the first quarter is an indicator of what is ahead for the stock market and the economy. Use the sample data in the file StockQuarter to answer the following.
a. Let $d_{i}$ denote the percentage change in price per share for company $i$ where
$$
d_{i}=\frac{\text {end of } 1^{\text {st}} \text {quarter price per share}-\text {beginning of } 1^{\text {st}} \text {quarter price per share}}{\text {beginning of } 1^{\text {st}} \text {quarter price per share}}
$$
Use the sample mean of these values to estimate the percentage change in the stock price over the first quarter.
b. What is the $95 \%$ confidence interval estimate of the population mean percentage change in the price per share of stock during the first quarter? Interpret this result.

Dominador Tan

Numerade Educator

Problem 23

Credit Card Expenditures. 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

Domestic Airfare. The Global Business Travel Association reported the domestic airfare for business travel for the current year and the previous year. 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

SAT Scores. The College Board SAT college entrance exam consists of two sections:
math and evidence-based reading and writing (EBRW). Sample data showing the math and EBRW 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 EBRW 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

PGA Tour Scores. 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 whether 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 $(\mathrm{a}) ?$ Explain.

Sheryl Ezze

Numerade Educator

Problem 27

Price Comparison of Smoothie Blenders. A personal fitness company produces both a deluxe and a standard model of a smoothie blender 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.
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.

Sheryl Ezze

Numerade Educator

Problem 29

Consider the hypothesis test
$$
\begin{array}{l}
H_{0}: p_{1}-p_{2} \leq 0 \\
H_{\mathrm{a}}: p_{1}-p_{2}>0
\end{array}
$$
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

Corporate Hiring Outlook. A BusinessWeek/Harris poll 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?

Sheryl Ezze

Numerade Educator

Problem 31

Impact of Pinterest on Purchase Decisions. Forbes reports that women trust recommendations from Pinterest more than recommendations from any other social network platform (Forbes.com). 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.

Sheryl Ezze

Numerade Educator

Problem 32

Mislabeling of Fish. 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). 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 proportions of tuna and mahi mahi that is mislabeled.

Sheryl Ezze

Numerade Educator

Problem 33

Voter Turnout. Minnesota had the highest turnout rate of any state for the 2016 presidential election (United States Election Project website). 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 2016 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 2016 presidential election.
b. What is the proportion of sampled registered voters in rural Minnesota that voted in the 2016 presidential election?
c. What is the proportion of sampled registered voters in urban Minnesota that voted in the 2016 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 Well Drilling. 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 2012 and 2018 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 2012 were more likely to be dry than wells drilled in 2018 .
b. What is the point estimate of the proportion of wells drilled in 2012 that were dry?
c. What is the point estimate of the proportion of wells drilled in 2018 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

Hotel Occupancy Rates. Tourism is extremely important to the economy of Florida. Hotel occupancy is an often-reported measure of visitor volume and visitor activity (Orlando Sentinel, May 19,2018 ). Hotel occupancy data for February in two consecutive years are as follows.
a. Formulate the hypothesis test that can be used to determine whether 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?

Sheryl Ezze

Numerade Educator

Problem 36

Gender Differences in Raise or Promotion Expectations. 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). 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 37

Default Rates on Bank Loans. Carl Allen and Norm Nixon are two loan offi-
cers at Brea Federal Savings and Loan Bank. The bank manager is interested in comparing the default rate on the loans approved by Carl to the default rate on the loans approved by Norm. In the sample of loans collected, there are 60 loans approved by Carl (9 of which defaulted) and 80 loans approved by Norm ( 7 of which defaulted).
a. State the hypothesis test that the default rates are the same for the two loan officers.
b. What is the sample default proportion for Carl? For Norm?
c. Use a .05 level of significance. What is the $p$ -value and what is your conclusion?

Sheryl Ezze

Numerade Educator

Problem 38

Supermarket Checkout Lane Design. 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?

Sheryl Ezze

Numerade Educator

Problem 39

SUV Lease Payments. Statista reports that the average monthly lease payment for an automobile is falling in the United States (Statista. com), but does this apply to all classes of automobiles? Suppose you are interested in whether this trend is true for sport utility vehicles (SUVs). The file SUVLease contains monthly lease payment data for 33 randomly selected SUVs in 2015 and 46 randomly selected $\mathrm{SUV}_{\mathrm{S}}$ in 2016
a. Provide and interpret a point estimate of the difference between the population mean monthly lease payments for the two years.
b. Develop a $99 \%$ confidence interval estimate of the difference between the mean monthly lease payments in 2015 and 2016 .
c. Would you feel justified in concluding that monthly lease payments have declined from 2015 to $2016 ?$ Why or why not?

Dominador Tan

Numerade Educator

Problem 40

Load versus No-Load Mutual Funds. Mutual funds are classified as load or $n o-$ 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 noload mutual funds. A sample of 30 load mutual funds and a sample of 30 no-load mutual funds were selected. Data in the file Mutual were collected on the annual return for the funds over a five-year period. The data for the first five load and first five no-load mutual funds are as follows.
a. Formulate $H_{0}$ and $H_{\mathrm{a}}$ such that rejection of $H_{0}$ leads to the conclusion that the load mutual funds have a higher mean annual return over the five-year period.
b. Conduct the hypothesis test. What is the $p$ -value? At $\alpha=.05,$ what is your conclusion?

Dominador Tan

Numerade Educator

Problem 41

Kitchen Versus Bedroom Remodeling costs. 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

Effect of Siblings on SAT Scores. In Born Together-Reared Apart: The Landmark Minnesota Twin Study, 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 evidence-based reading and writing (EBRW) SAT scores for several pairs of identical twins (twins who share all of their genes) and were raised separately, 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 EBRW 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 EBRW 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

Change in Financial Security. Country Financial, a financial services company, uses surveys of adults age 18 and older to determine whether personal financial fitness is changing over time. A recent sample of 1000 adults showed 410 indicating that their financial security was more than fair. Just a year prior, 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. Conduct the hypothesis test and compute the $p$ -value. At a .05 level of significance, what is your conclusion?
c. What is the $95 \%$ confidence interval estimate of the difference between the two population proportions? What is your conclusion?

Sheryl Ezze

Numerade Educator

Problem 44

Differences in Insurance Claims Based on Marital Status. 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 $\alpha=.05 .$ 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.

Sheryl Ezze

Numerade Educator

Problem 45

Drug-Resistant Gonorrhea. Each year, over 2 million people in the United States become infected with bacteria that are resistant to antibiotics. In particular, the Centers of Disease Control and Prevention has launched studies of drug-resistant gonorrhea ( $C D C$. gov website $)$. Of 142 cases tested in Alabama, 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?

Sheryl Ezze

Numerade Educator

Problem 46

News Access Via Computer. The American Press Institute reports that almost $70 \%$ of all American adults use a computer to gain access to news. Suppose you suspect that the proportion of American adults under 30 years old who use a computer to gain access to news exceeds the proportion of Americans at least 30 years old who use a computer to gain access to news. Data in the file ComputerNews represent responses to the question "Do you use a computer to gain access to news?" given by random samples of American adults under 30 years old and Americans who are at least 30 years old.
a. Estimate the proportion of American adults under 30 years old who use a computer to gain access to news and the proportion of Americans at least 30 years old who use a computer to gain access to news.
b. Provide a $95 \%$ confidence interval for the difference in these proportions.
c. On the basis of your findings, does it appear the proportion of American adults under 30 years old who use a computer to gain access to news exceeds the proportion of Americans who are at least 30 years old that use a computer to gain access to news?

Dominador Tan

Numerade Educator

Problem 47

For the week ended January $15,2009,$ the bullish sentiment of individual investors was $27.6 \%$ (AAII Journal). The bullish sentiment was reported to be $48.7 \%$ one week earlier and $39.7 \%$ one month earlier. The sentiment measures are based on a poll conducted by the American Association of Individual Investors. Assume that each of the bullish sentiment measures was based on a sample size of 240 .
a. Develop a $95 \%$ confidence interval for the difference between the bullish sentiment measures for the most recent two weeks.
b. Develop hypotheses so that rejection of the null hypothesis will allow us to conclude that the most recent bullish sentiment is weaker than that of one month ago.
c. Conduct a hypotheses test of part (b) using $\alpha=.01$. What is your conclusion?

Sheryl Ezze

Numerade Educator