Assume that we have selected two independent random samples from populations having proportions p1 and p2 and that E = 800/1000 = .8 and :52 = 950/1000 = .95. Test H0: p1 pz 2 .12 versus Ha: p1 p2 |t| 0 . 0002* Lower CL Dif -1. 3986 Prob > t 0. 9999 Confidence 0. 95 Prob 3 equals 0.1316. Use the pvalue to test these hypotheses with 0 equal to .10, .05, .01, and .001. How much evidence is there that pd exceeds 3? What does this say about the size of the difference between ,u1 and [12? (Round your p-value answer to 4 decimal places.) p = Reject H0 at or equal to , evidence that p1 and u2 differ by more than 3. In the book Essentials ofMarketing Research, William R. Dillon, Thomas J. Madden, and Neil H. Firtle discuss a research proposal in which a telephone company wants to determine whether the appeal of a new security system varies between homeowners and renters. Independent samples of140 homeowners and 60 renters are randomly selected. Each respondent views a TV pilot in which a test ad for the new security system is embedded twice. Afterward, each respondent is interviewed to nd out whether he or she would purchase the security system. Results show that 25 out of the 140 homeowners denitely would buy the security system, while 9 out of the 60 renters definitely would buy the system. (a) Letting p1 be the proportion of homeowners who would buy the security system, and letting p2 be the proportion of renters who would buy the security system, set up the null and alternative hypotheses needed to determine whether the proportion of homeowners who would buy the security system differs from the proportion of renters who would buy the security system. H0: p1 p2 I 'versus Ha: p1 p2 l ' (b) Find the test statistic z and the ovalue for testing the hypotheses of part a. Use the pvalue to test the hypotheses with 0' equal to .10, .05, .01, and .001. How much evidence is there that the proportions of homeowners and renters differ? (Round the intermediate calculations to 3 decimal places. Round your 2 value to 2 decimal and p -value to 3 decimal places.) 2: p - value = Reject HO at a = , but not at a = evidence that p1 and p2 differ. (c) Calculate a 95 percent confidence interval for the difference between the proportions of homeowners and renters who would buy the security system. On the basis of this interval, can we be 95 percent confident that these proportions differ? (Round your answers to confidence interval to 4 decimal places. Negative amounts should be indicated by a minus sign. ) Confidence interval =An article in Fortune magazine reported on the rapid rise of fees and expenses charged by mutual funds. Assuming that stock fund expenses and municipal bond fund expenses are each approximately normally distributed, suppose a random sample of 12 stock funds gives a mean annual expense of1.63 percent with a standard deviation of .31 percent, and an independent random sample of12 municipal bond funds gives a mean annual expense of 0.89 percent with a standard deviation of.23 percent. Let [41 be the mean annual expense for stock funds, and let [.12 be the mean annual expense for municipal bond funds. Do parts a, b, and c by using the equal variances procedure. (a) Set up the null and alternative hypotheses needed to attempt to establish that the mean annual expense for stock funds is larger than the mean annual expense for municipal bond funds. Test these hypotheses at the .05 level of signicance. (Round your 5P2 answer to 4 decimal places and t-value to 2 decimal places.) H0: [11 - [12 versus Ha: p1 - u2 52p 1: 6.64 H0 with a = 0.05 (b) Set up the null and alternative hypotheses needed to attempt to establish that the mean annual expense for stock funds exceeds the mean annual expense for municipal bond funds by more than .5 percent. Test these hypotheses at the .05 level of significance. (Round your t-value to 2 decimal places and other answers to 1 decimal place.) H0:p1 p2 \"versus Ha: p1 112 r t= H0 with a = 0.05 (c) Calculate a 95 percent condence interval for the difference between the mean annual expenses for stock funds and municipal bond funds. Can we be 95 percent confident that the mean annual expense for stock funds exceeds that for municipal bond funds by more than .5 percent? (Round your answers to 3 decimal places.) The interval = [ r . r l' ]. r , the interval is r l' 0.5