Exercise 14.6: Consider the hypothesis test - Ho: PI-P2 SO Ha: P1-P2 > 0 The following results are for independent samples taken from the two populations. Sample 1 Sample 2 a. Find p = Pini+Pzz n1+n2 n1 = 200 n2 = 300 b. Find Test Statistic Z p1 = 0.22 p2 =0.16 c. Find p-valued d. Given a = 0.05, what is your conclusion? Exercise 14.7: At a = .10, testing the hypothesis that the proportion of consumer industry companies' (CON) winter-quarter profit growth is more than 2 percent greater than the proportion of banking companies' (BKG) winter-quarter profit growth ( Peay > 0.02+PBKG), given that P CON =.20, PBKG =14, Ucox = 300, and Doxa = 400, can we reject the null hypothesis? Step 1: Ho VS HA Step 3: Do = So, Spi -pz Test Statistic Z = Step 4: Critical Values = Step 5.1: Reject Ho or Do not reject Ho Step 5.2: Write down your conclusion in simple English sentences. Is the proportion of consumer industry companies' (CON) winter-quarter profit growth is more than 2 percent greater than the proportion of banking companies' (BKG) winter-quarter profit growth? Exercise 14.8: Use table A6-A9, on pages 795-798, to find the following Fa points: a. F.os with df1 = 5 and df2 = 10 b. F.or with df1 = 8 and df2 = 12 c. F.10 with df1 = 8 and df2 = 12Exercise 14.9: Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobile. A researcher is interested in finding out whether the variance of the annual repair costs also increases with the age of automobile. A sample of 25 automobiles 4 years old showed a sample standard deviation for annual repair costs of $ 170, and a sample of 26 automobiles 2 years old showed a sample standard deviation for annual repair cost of $ 100. a. State the null and alternative versions of the research hypothesis that the variance in annual repair cost is larger for the older automobiles. b. At a 0.01 level of significance, what is your conclusion, using the critical value approach? c. Given the p-value of 0 0057, corresponding to test statistic F, and at a 0.01 level of significance, what is your conclusion? Exercise 14.10: The variability in the amount of impurities present in a batch of chemicals' used for a particular process depends on the length of time that the process is in operation. Suppose a sample of size 25 is drawn from the normal process which is to be compared to a sample of a new process that has been developed to reduce the variability of impurities. (a = 0.05) Sample 1 (Original Process) Sample 2 (New Process) Sample size 25 25 Sample Variance 1.04 0.51 Conduct a 5-Step F-Test to determine whether the variability in the original process is greater than the variability in the new process. Step 1: State Ho and HA Step 2: a = 0.05 Step 3: Test Statistic F dfi = df2 = Step 4: Label the value of the critical value in F on the bottom axis. Draw and shade the appropriate rejection region. State the decision rule Step 5.1: Reject Ho or Do not reject Ho Step 5.2: Write down your conclusion in simple English sentences. Is the variability in the original process is greater than the variability in the new process