MATH 534 Week 5 Homework Problems

1. Question: In hypothesis testing the statistical conclusion is either to reject or not to reject the null hypothesis based on the sample data. Which of the following statements is true? 2. Question: If a company wants to prove that the proportion (p) of its revenues from overseas operations is more than 18%, the null and alternate hypotheses are __________. 3. Question: A test of the hypotheses, H0: p = 0.18 and H1: p 0.18 is a _____________. 4. Question: The dean of a business school claims that the average starting salary of its graduates is more than 85(in $000’s). It is known that the population standard deviation is 10 (in $000’s). Sample data on the starting salaries of 64 randomly selected recent graduates yielded a mean of 88(in $000s). What is the value of the sample test statistic? 5. Question: The dean of a business school claims that the average starting salary of its graduates is more than 85 (in $000’s). It is known that the population standard deviation is 10 (in $000’s). Sample data on the starting salaries of 64 randomly selected recent graduates yielded a mean of 88 (in $000s). What is the p-value for the hypothesis test to check out the dean’s claim? 6. Question: The probability of getting a test statistic as extreme as the observed test statistic computed from the sample data under the assumption that the null hypothesis is true is called the _________. 7. Question: A researcher is testing a hypothesis of a single mean. The critical z value for α = .05 and a two-tailed test is +1.96. The observed z value from sample data is -1.85. The decision made by the researcher based on this information is to ___________ the null hypothesis. 8. Question: According to one survey taken a few years ago, 32% of American households have attempted to reduce their long-distance phone bills by switching long-distance companies. Suppose that business researchers want to test to determine if this figure is still accurate today by taking a new survey of 80 American households who have tried to reduce their long-distance bills. Suppose further that of these 80 households, 26% say they have tried to reduce their bills by switching long-distance companies. Is this result enough evidence to state that a significantly different proportion of American households are trying to reduce long-distance bills by switching companies? 9. Question: According to Zero Population Growth, the average urban U.S. resident consumes 3.3 pounds of food per day. Is this figure accurate for rural U.S. residents? Suppose 64 rural U.S. residents are identified by a random procedure and their average consumption per day is 3.60 pounds of food. Assume a population variance of 1.31 pounds of food per day. Use a 5% level of significance to determine whether the Zero Population Growth figure for urban U.S. residents also is true for rural U.S. residents on the basis of the sample data. 10. Question: A computer manufacturer estimates that its line of minicomputers has, on average, 8.7 days of downtime per year. To test this claim, a researcher contacts seven companies that own one of these computers and is allowed to access company computer records. It is determined that, for the sample, the average number of downtime days is 5.9, with a sample standard deviation of 1.1 days. Assuming that number of downtime days is normally distributed, test to determine whether these minicomputers actually average 8.7 days of downtime in the entire population. 11. Question: A coffee-dispensing machine is supposed to deliver 8 ounces of liquid into each paper cup, but a consumer believes that the actual mean amount is less. The consumer obtained a sample of 16 cups of the dispensed liquid with sample mean of 7.75 ounces and sample variance of 0.81 ounces. If the dispensed liquid delivered per cup is normally distributed, the appropriate decision at α=0.05 is 12. Question: Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of email messages sent by GFS employees are not business related. A random sample of 300 e-mail messages was selected to test this hypothesis at the 0.01 level of significance. Fifty-four of the messages were not business related. The appropriate decision is _________. 13. Question: The customer help center in your company receives calls from customers who need help with some of the customized software solutions your company provides. Your company claims that the average waiting time is 7 minutes at the busiest time, from 8 a.m. to 10 a.m., Monday through Thursday. One of your main clients has recently complained that every time she calls during the busy hours, the waiting time exceeds 7 minutes. You conduct a statistical study to determine the average waiting time with a sample of 35 calls for which you obtain an average waiting time of 8.15 minutes. If the population standard deviation is known to be 4.2 minutes, and α = 0.05, the appropriate decision is: