Professors collected data consisting of eye color and gender of statistics students. Among 876 male students, 347 had blue eyes. Among 1059 female students, 418 had blue eyes. Use a 0.05 significance level to test the claim that the proportions of blue eyes are the same for males and females. Complete parts (a) through (c) below. Consider the first sample to be the sample of males and the second sample to be the sample of females. a. Test the claim using a hypothesis test. What are the null and alternative hypotheses for the hypothesis test? OA. Ho: P1 = P2 O B. Ho: P1 # P2 O C. Ho: P1 = P2 H 1 : P1 > P2 H1: P1 = P2 H1 : P1 # P2 OD. Ho: P1 = P2 OE. Ho: P1 SP2 OF. Ho: P1 2 P2 H1: P1 = P2 H1: P1 7 P2 H1 : P1 # P2 Identify the test statistic. 2= (Round to two decimal places as needed.) Identify the P-value. P-value = (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? The P-value is the significance level of a = 0.05, so the null hypothesis. There evidence to warrant rejection of the claim that the proportions of blue eyes are the same for females and males. b. Test the claim by constructing an appropriate confidence interval. The 95% confidence interval is | H2 Hy : Hy H2 The test statistic, t, is . (Round to two decimal places as needed.) The P-value is .(Round to three decimal places as needed.) State the conclusion for the test. O A. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that giving candy does result in greater tips. O B. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that giving candy does result in greater tips. O C. Reject the null hypothesis. There is not sufficient evidence to support the claim that giving candy does result in greater tips. O D. Reject the null hypothesis. There is sufficient evidence to support the claim that giving candy does result in greater tips. b. Construct the confidence interval suitable for testing the claim in part (a).

H2 The test statistic, t, is . (Round to two decimal places as needed.) The P-value is . (Round to three decimal places as needed.) State the conclusion for the test. O A. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. O B. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. O C. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. O D. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. b. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.