Reis, Inc., a New York real estate research firm, tracks the cost of apartment rentals in the United States. In mid-2002, the nationwide mean apartment rental rate was $895 per month (The Wall Street Journal, July 8, 2002). Assume that, based on the historical quarterly surveys, a population standard deviation of σ = $225 is reasonable. In a current study of apartment rental rates, a sample of 180 apartments nationwide provided a sample mean of $915 per month. Do the sample data enable Reis to conclude that the population mean apartment rental rate now exceeds the level reported in 2002?
a. State the null and alternative hypotheses.
b. Determine the p-value
c. At alpha = .01, explain your conclusion.
d. Provide a recommendation for Reis to consider at this time.
U.S. Department of Labor
In 2001, the U.S. Department of Labor reported the average hourly earnings for U.S. production workers to be $14.32 per hour (The World Almanac 2003). A sample of 75 production workers during 2003 showed a sample mean of $14.68 per hour.
a. Assuming a population standard deviation of $1.45, determine if it can be concluded that an increase occurred in the mean hourly earnings since 2001. Use alpha = .05.
Nielsen Media Research
AOL Time Warner Inc.'s CNN has been the longtime ratings leader of cable television news. Nielsen Media Research indicated that the mean CNN viewing audience was 600,000 viewers per day during 2002 (The Wall Street Journal, March 10, 2003). Assume that for a sample of 40 days during the first half of 2003, the daily audience was 612,000 viewers with a sample standard deviation of 65,000 viewers.
a. Develop the hypotheses if CNN management would like information on any change in the CNN viewing audience.
b. Determine the p-value.
c. Select a level of significance. Explain your conclusion.
d. Provide a recommendation to CNN management in this application.
J.C. Adams Company
The J.C. Adams Co., a mail-order firm that deals in small gifts, charges a flat rate for postage regardless of the weights of the packages. The flat postage charge is the current postage rate per ounce times 16.90. The company management assumes that in the long run the firm will break even on postage costs. The accounting department disputes the fixed postage charge and suggests that it should be changed. Management, however, wishes to be at least 95% certain that a policy change is justified since it may incur postage losses or be unattractive to potential customers. Further, management wishes to be 99% certain that if a policy change is made, the change will not incur losses due to insufficient postage charges to customers. Management decides to take a random sample of the weights of 100 packages mailed this month and base the decision on the sample results. The sample indicates a mean weight of 17.8 ounces and a standard deviation of 3.2 ounces.
a. Determine the action to be taken by J. C. Adams Company, if any, and explain your conclusion.
This soluton shows all calculations and explanations for four hypothesis tests.