Answer Happy

A survey of 700 adults from a certain region asked, "Do you enjoy shopping for clothing for yourself?" The results indicated that 55% of the females enjoyed shopping for clothing for themselves as compared to 48% of the males. The sample sizes of males and females were not provided. Suppose that of 400 females, 220 said that they enjoyed shopping for clothing for themselves while of 300 males, 144 said that they enjoyed shopping for clothing for themselves. Complete parts (a) through (d) below.

a. Is there evidence of a difference between males and females in the proportion who enjoy shopping for clothing for themselves at the 0.01 level of significance? State the null and alternative hypotheses, where , is the population proportion of females that enjoy shopping for themselves and It, is the population proportion of males that enjoy shopping for themselves. O A. Ho: 11 *12 H₃: Its < 12 OC. Ho -T2 H₃: Is < 12 O E. Ho: 11 =12 H:14 12 OB. Ho: 1,712 Hp : Tg > 72 D. Ho: 19 =12 H:17 12 OF HO 11 #12 H:11 =12 Determine the value of the test statistic ZSTAT = 2.33 (Round to two decimal places as needed.) Determine the critical value(s) for this test of hypothesis. The critical value(s) is (are) 2.58,- 2.58 (Round to two decimal places as needed. Use a comma to separate answers as needed.) State the conclusion. Do not reject the null hypothesis. There is insufficient evidence to support the claim that there is a difference between males and females in the proportion who enjoy shopping for clothing for themselves. b. Find the p-value in (a) and interpret its meaning The p-value in part (a) is 0.020" (Round to three decimal places as needed.) What does the p-value mean? O A. The p-value is the probability that the null hypothesis is true. OB. The p-value is the probability of rejecting the null hypothesis if the test were repeated for different samples. C. The p-value is the probability of obtaining a result at least as extreme as the one obtained with this sample given that the null hypothesis is true. OD. The p-value is the probability of falsely rejecting the null hypothesis.

c. Construct and interpret a 99% confidence interval estimate for the difference between the proportion of males and females who enjoy shopping for clothing for themselves. The confidence interval is -0.0072 to 0.1472 (Round to four decimal places as needed.) What does the confidence interval mean? contained in the interval. A researcher can be 99% confident that the difference in the population proportions of males and females that enjoy shopping for themselves is d. What are the answers to (a) through (c) if 258 males enjoyed shopping for clothing for themselves? Is there evidence of a difference between males and females in the proportion who enjoy shopping for clothing for themselves at the 0.01 level of significance? State the null and alternative hypotheses, where ty is the population proportion of females that enjoy shopping for themselves and Ty is the population proportion of males that enjoy shopping for themselves. O B. Ho a ta O A. Ho: 1 =12 H:11<12 на: 11 < 12 OD. H: 1*12 O c. Hoit, Eth H₂ : 2 = 12 н: п1 > 12 OF. Ho: 1 = 12 E. Ho: 1, 12 H₃: Is the H: 1, 712 Determine the value of the test statistic. ZSTAT = 1.33 (Round to two decimal places as needed.) Determine the critical value(s) for this test of hypothesis. The critical value(s) is (are) 2.58, -2.58 (Round to two decimal places as needed. Use a comma to separate answers as needed.) State the conclusion. Do not reject the null hypothesis. There is insufficient evidence to support the claim that there is a difference between males and females in the proportion who enjoy shopping for clothing for themselves. Find the p-value and interpret its meaning. The p-value is 0.184 (Round to three decimal places as needed.)

What does the p-value mean? The probability of obtaining a difference in proportions that gives rise to a test statistic equal to or more extreme than the test statistic is equal to the p-value if there is no difference between the population proportions of males and females that enjoy shopping for themselves. Construct and interpret a 99% confidence interval estimate for the difference between the proportion of males and females who enjoy shopping for clothing for themselves. The confidence interval is -0.0376 to 0.1176 (Round to four decimal places as needed.) What does the confidence interval mean? A researcher can be 99% confident that the difference in the population proportions of males and females that enjoy shopping for themselves is contained in the interval