A random sample is obtained from a population with a variance of σ^2 = 400 and the sample mean is computed to be x̄ = 70. Consider the null hypothesis H0: µ = 80 versus the alternative hypothesis H1: µ < 80. Compute the p-value for the following options: a. Sample size n = 25 b. Sample size n = 16 c. Sample size n = 44 d. Sample size n = 32.
9.11) A manufacturer of detergent claims that the contents of boxes sold weigh on average at least 16 ounces. The distribution of weight is known to be normal, with a standard deviation of 0.4 ounce. A random sample of 16 boxes yielded a sample mean weight of 15.84 ounces. Test at the 10% significance level the null hypothesis that the population mean weight is at least 16 ounces.
9.15) Test the hypotheses, H0: µ = 100 and H1: µ < 100 using a random sample of n = 36, a probability of Type I error equal to 0.05, and the following sample statistics. a. x̄ = 106, s = 15 b. x̄ = 104, s = 10 c. x̄ = 95, s = 10 d. x̄ = 92, s = 18.
9.19) A random sample of 172 marketing students was asked to rate, on a scale from 1 (not important) to 5 (extremely important), health benefits as a job characteristic. The sample mean rating was 3.31, and the sample standard deviation was 0.7. Test at the 1% significance level the null hypothesis that the population mean rating is at most 3 against the alternative that it is larger than 3.
9.23) A company selling licenses for new e-commerce computer software advertises that firms using the software obtain, on average during the first year, a yield of 10% on their initial investments. A random sample of 10 of these franchises produced the following yields for the first year of operation: 6.1, 9.2, 11.5, 8.6, 12.1, 3.9, 8.4, 10.1, 9.4, 8.9. Assuming that population yields are normally distributed, test the company's claim.
9.31) In a random sample of 998 adults in the US, 17.3% of the sample members indicated some measure of disagreement with this statement.