Q1. According to a study several years ago, the average BMW driver earns $82 600 per year. Suppose a researcher believes that the average annual earnings of a BMW driver are lower now, and he sets up a study in an attempt to prove his theory. He randomly samples 18 BMW drivers and finds out that the average annual salary for this sample is $78 974, with a population standard deviation of $7810. Use α = .01 to test the researcher's theory. Assume annual salaries are normally distributed.
Q2. Suppose a null hypothesis is that the population mean is greater than or equal to 100. Suppose further that a random sample of 48 items is taken and the population standard deviation is 14. For each of the following α values, compute the probability of committing a Type II error if the population mean actually is 99.
a. α = .10
b. α = .05
c. α = .01
d. Based on the answers to parts (a), (b) and (c), what happens to the value of β as α gets smaller?
Q3. Suppose you are testing H0: p = .29 versus Ha: p ≠ .29. A random sample of 740 items shows that 207 have this characteristic. With a .05 probability of committing a Type I error, test the hypothesis. For the p-value method, what is the probability of the calculated z value for this problem? If you had used the critical value method, what would the two critical values be? How do the sample results compare with the critical values?
Q4. Where do CFOs get their money news? According to Robert Half International, 47% get their money news from newspapers, 15% get it from communication/colleagues, 12% get it from television, 11% from the internet, 9% from magazines, 5% from radio and 1% don't know. Suppose a researcher wants to test these results. She randomly samples 67 CFOs and finds that 40 of them get their money news from newspapers. Does the test show enough evidence to reject the findings of Robert Half International? Use α = .05