Question

ASK YOUR TEACHER It is thought that the front cover and the nature of the first question on mail surveys influence the response rate. An article tested this theory by experimenting with different cover designs. One cover was plain; the other used a picture of a skydiver. The researchers speculated that the return rate would be lower for the plain cover. Number Sent Cover Plain Skydiver 203 213 Number Returned 101 108 Does this data support the researchers' hypothesis? Test the relevant hypotheses using a = 0.10 by first calculating a P-value. State the relevant hypotheses. (Use p, for the plain cover and P2 for the skydiver cover.) OH!P1 - P2 = 0 H: Pi-P2 > 0 O Ho: P1-P2 = 0 H:P- P25 Oo oo Ho: P1-P2 = 0 H: P1 P2 = 0 H: P1 - P20 Ho: P: Compute the test statistic value and find 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. Reject Ho. The data suggests that the front cover and nature of the first question on mail surveys does influence the response rate. O Reject Ho. The data does not suggest that the front cover and nature of the first question on mail surveys influence the response rate. Fail to reject Ho. The data does not suggest that the front cover and nature of the first question on mail surveys influence the response rate. Fail to reject Ho. The data suggests that the front cover and nature of the first question on mail surveys does influence the response rate. You may need to use the appropriate table in the Appendix of Tables to answer this question. Need Help? Read It Talk to a Tutor

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 - p2 =0
Alternate Hypothesis, Ha: p1 - p2 > 0

p1cap = X1/N1 = 101/203 = 0.4975
p2cap = X2/N2 = 108/213 = 0.507
pcap = (X1 + X2)/(N1 + N2) = (101+108)/(203+213) = 0.5024

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.4975-0.507)/sqrt(0.5024*(1-0.5024)*(1/203 + 1/213))
z = -0.19

P-value Approach
P-value = 0.4247
As P-value >= 0.1, fail to reject null hypothesis.

Fail to reject H0. The data does not support the claim