1. 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 the apartment rental rates shown in the CD file named RentalRates. 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. At α=_ .01, what is your conclusion?
c. What would you recommend Reis consider doing at this time?
2. Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean time of 15 minutes or less. If a longer mean survey time is necessary, a premium rate is charged. A sample of 35 surveys provided the survey times shown in the CD file named Fowle. Based upon past studies, the population standard deviation is assumed known with σ =4 minutes. Is the premium rate justified?
a. Formulate the null and alternative hypotheses for this application.
b. Compute the value of the test statistic.
c. At α _ .01, what is your conclusion?
3. The Employment and Training Administration reported the U.S. mean unemployment insurance benefit of $238 per week (The World Almanac, 2003). A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was below the national level.
a. Develop appropriate hypotheses such that rejection of H0 will support the researcher's
contention.
b. For a sample of 100 individuals, the sample mean weekly unemployment insurance
benefit was $231 with a sample standard deviation of $80. At α = .05, what is your conclusion?
c. Repeat the preceding hypothesis test using the critical value approach.
4. A study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands. To investigate whether this result applies to its own product, the manufacturer of a national name-brand ketchup asked a sample of shoppers whether they believed that supermarket ketchup was as good as the national brand ketchup.
a. Formulate the hypotheses that could be used to determine whether the percentage of supermarket shoppers who believe that the supermarket ketchup was as good as the national brand ketchup differed from 64%.
b. If a sample of 100 shoppers showed 52 stating that the supermarket brand was as good as the national brand, at α=_ .05, what is your conclusion? Should the national brand ketchup manufacturer be pleased with this conclusion? Explain.