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?

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.

What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females?

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.

$$\begin{array} { r l } { \text { Tampa } } & { \text { Dallas } } \\ { n _ { 1 } = 40 } & { n _ { 2 } = 50 } \\ { \overline { x } _ { 1 } = \$ 56,100 } & { \overline { x } _ { 2 } = \$ 59,400 } \\ { s _ { 1 } = \$ 6000 } & { s _ { 2 } = \$ 7000 } \end{array}$$

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.

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.

$$\begin{array}{ll} {\text { Tampa }} & {\text { Dallas }} \\ n_1=40 & n_2=50 \\ \bar{x}_1=\$ 56,100 & \bar{x}_2=\$ 59,400 \\ s_1=\$ 6000 & s_2=\$ 7000 \end{array}$$

d. What is your conclusion?

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.

$$\begin{array}{ll} {\text { Tampa }} & {\text { Dallas }} \\ n_1=40 & n_2=50 \\ \bar{x}_1=\$ 56,100 & \bar{x}_2=\$ 59,400 \\ s_1=\$ 6000 & s_2=\$ 7000 \end{array}$$

b. What is the value of the test statistic?

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.

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?

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.

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?

What is the $95 \%$ confidence interval for the difference between the two population means?

The mean annual premium for automobile insurance in the United States is $\$ 1503$. Being from Pennsylvania, you believe automobile insurance is cheaper there and wish to develop statistical support for your opinion. A sample of 25 automobile insurance policies from the state of Pennsylvania showed a mean annual premium of $\$ 1440$ with a standard deviation of $s=\$ 165$.

b. What is a point estimate of the difference between the mean annual premium in Pennsylvania and the national mean?

Researchers at Purdue University and Wichita State University found that airlines are doing a better job of getting passengers to their destinations on time. 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 DATAfile named AirDelay. Data are displayed for both airlines.

c. Using a $.05$ level of significance, what is the $p$-value, and what is your conclusion?

Annual per capita consumption of milk is 21.6 gallons (Statistical Abstract of the United States: 2006). Being from the Midwest, you believe milk consumption is higher there and wish to support your opinion. A sample of 16 individuals from the midwestern town of Webster City showed a sample mean annual consumption of 24.1 gallons with a standard deviation of s = 4.8.

What is a point estimate of the difference between mean annual consumption in Webster City and the national mean?

Annual per capita consumption of milk is 21.6 gallons (Statistical Abstract of the United States: 2006). Being from the Midwest, you believe milk consumption is higher there and wish to support your opinion. A sample of 16 individuals from the midwestern town of Webster City showed a sample mean annual consumption of 24.1 gallons with a standard deviation of s = 4.8.

At $\alpha$= .05, test for a significant difference. What is your conclusion?

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 (currently 75.7), studies show its shares have a good chance of outperforming the broad stock market in the long run” (Business- Week, March 2, 2009). The following satisfaction scores of three companies for the 4th quarters of 2007 and 2008 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.

$$\begin{matrix} \text{Company} & \text{2007 Score} & \text{2008 Score}\\ \text{Rite Aid} & \text{73} & \text{76}\\ \text{Expedia} & \text{75} & \text{77}\\ \text{J.C. Penney} & \text{77} & \text{78}\\ \end{matrix}$$

a. For Rite Aid, is the increase in the satisfaction score from 2007 to 2008 statistically significant? Use $\alpha$= .05. What can you conclude? b. Can you conclude that the 2008 score for Rite Aid is above the national average of 75.7? Use $\alpha$= .05. c. For Expedia, is the increase from 2007 to 2008 statistically significant? Use $\alpha$= .05. d. When conducting a hypothesis test with the values given for the standard deviation, sample size, and α, how large must the increase from 2007 to 2008 be for it to be statistically significant? e. Use the result of part (d) to state whether the increase for J.C. Penney from 2007 to 2008 is statistically significant.

Annual per capita consumption of milk is 21.6 gallons (Statistical Abstract of the United States: 2006). Being from the Midwest, you believe milk consumption is higher there and wish to support your opinion. A sample of 16 individuals from the midwestern town of Webster City showed a sample mean annual consumption of 24.1 gallons with a standard deviation of s = 4.8.

Develop a hypothesis test that can be used to determine whether the mean annual consumption in Webster City is higher than the national mean.

Which is cheaper: eating out or dining in? The mean cost of a flank steak, broccoli, and rice bought at the grocery store is $13.04 (Money.msn website, November 7, 2012). A sample of 100 neighborhood restaurants showed a mean price of$12.75 and a standard deviation of $2 for a comparable restaurant meal.

a. Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean cost of a restaurant meal is less than fixing a comparable meal at home.

b. Using the sample from the 100 restaurants, what is the p-value?

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

d. Repeat the preceding hypothesis test using the critical value approach.