1. The daily car rental rates for a sample of eight cities follow.
a. What is the 98% confidence interval estimate of the variance of car rental rates for the population?
b. What is the 99% confidence interval estimate of the standard deviation for the population?
2. At the end of 2008, the variance in the semiannual yields of overseas government bond was σ 2 = 0.25. A group of bond investors met at that time to discuss future trends in overseas bond yields. Some expected the variability in overseas bond yields to increase and others took the opposite view. The following table shows the semiannual yields for 12 overseas countries as of March 6, 2009.
a. Compute the mean, variance, and standard deviation of the overseas bond yields as of March 6, 2009.
b. Develop hypotheses to test whether the sample data indicate that the variance in bond yields has increased from that at the end of 2008.
c. Use α = .025 to conduct the hypothesis test formulated in part (b). What is your conclusion?
3. Find the critical values based on F distribution when variance of sample 1 is greater than variance of sample 2. Alpha and Sample Sizes are given below.
a. α = .05 with n1 = 6 and n2 = 11
b. α = .025 with n1 = 21 and n2 = 26
c. α = .01 with n1 = 61 and n2 = 61
d. α = .10 with n1 = 9 and n2 = 25
4. The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for two machines. Use a .02 level of significance. What is your conclusion? Which machine of the two provides the greater opportunity for quality improvements?
5. Fidelity Magellan is a large cap growth mutual fund and Fidelity Small Cap Stock is a small cap growth mutual fund. For Fidelity Magellan, the sample standard deviation is 18.89; for Fidelity Small Cap Stock, the sample standard deviation is 13.03. The standard deviation for both funds was computed based on a sample of sizes 26 and 25 respectively. Financial analysts often use the standard deviation as a measure of risk. Conduct a hypothesis test to determine whether the large cap growth fund is riskier than the smaller cap growth fund. Use α = .10 as the level of significance.