Question

A plan for an executive travelers' club has been developed by an airline on the premise that 5% of its current customers would qualify for membership. A random sample of 500 customers yielded 39 who would qualify (a) Using this data, test at level 0.01 the null hypothesis that the com pany's premise is correct against the alternative that it is not correct. State the appropriate null and alternative hypotheses. Ho: p 0.05 Ha: p 0.05 O Ho: p 0.05 Ha p 0.05 OHo: p 0.05 Ha: p 0.05 OHo: p 0.05 Ha: p0.05 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) P-value State the conclusion in the problem context O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the company's premise is incorrect. O Reject the null hypothesis. There is sufficient evidence to conclude that the company's premise is incorrect. ODo not reject the null hypothesis. There is sufficient evidence to conclude that the company's premise is incorrect. OReject the null hypothesis. There is not sufficient evidence to conclude that the company's premise is incorrect (b) What is the probability that when the test of part (a) is used, the company's premise will be judged correct when in fact 10% of all current customers qualify. (Round your answer to four decimal places.)

I need the Z and P-value also part B answered. Double-check your work as I don't know but I managed to get this wrong a few times. Thank you!

Answer 1

p= 0,058 = 0.078 - Ans: n=500, X=39 a) Ho: p=0.05 Ha : P = 0.05 0.078-0.05 2.87 0.050,-0.05) n 500 alue = P-value = (0.004) - Sonce p-value <a 10.01) Refect the noll hypothesis. There is sufficient endence to conclude that the company's please as Ion Correct.