4. [6/11 Points] DETAILS PREVIOUS ANSWERS UHSTATS 12.E.051 .5. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A certain magazine reported that in a survey of 500 randomly selected adult American Catholics, 60% answered yes to the question "Do you favor allowing women to be priests?" IA uses (a) Set up the null and alternative hypotheses for deciding whether more than half of American Catholics favor allowing women to be priests. Ho: p I 0.5 Ha: p > v 0.5 (b) What conditions are necessary for using a z-statistic to test the hypotheses in part (a)? (Select all that apply.) The sample size must be large enough. _ npo and n(1 p0) must be less than 10. : The sample must be randomly selected. There are no requirements. The sample size must not be too big. _ npo and n(1 p0) must be greater than 10. Are those conditions met here? Yes O No 0 There are no requirements. v (c) Compute the test statistic for this situation. (Round your answer to two decimal places.) 2 = 0.15 X _J The sample size must not be too big. Are those conditions met here? Yes 0 No 0 There are no requirements. i 3 npo and n(1 p0) must be greater than 10. (c) Compute the test statistic for this situation. (Round your answer to two decimal places.) z = 0.15 x (d) Estimate the p-value for the test. (Round your answer to four decimal places.) (e) On the basis of the p-value, make a conclusion for this situation. Rejectthe null hypothesis v q because the p-value is smaller v than 0.05. (f) Calculate a 95% condence interval for the proportion of American Catholics who favor allowing women to be priests. Does this confidence interval confirm the conclusion that a majority of American Catholics favor allowing women priests? Explain. (Round your answers to three decimal places.) The condence interval is t0 . This conrms v the conclusion that a majority of adult American Catholics favor allowing women priests