It is thought that the front cover and the nature of the first question on mail

Question

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 Cover Plain Skydiver Number Sent 208 211 Number Returned 101 109 Does this data support the researchers' hypothesis? Test the relevant hypotheses using . 0.10 by first calculating a P-value. State the relevant hypotheses. (Use pi for the plain cover and p2 for the skydiver cover.) Ho: p1 -P2-0 Ha P1 P2 0 0 H0: P1-P2=0 Ha P1 P20 @ Ho: ! _ P2.0 Ha P1 p2 0 Ho: p1-P2 0 Ha P1 P20 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 em context. Reject HO·The data does not suggest that the front cover and nature of the first question on mail surveys influence the response rate. O Reject Ho. The data suggests that the front cover and nature of the first question on mail surveys does 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. 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.

Explanation / Answer

Solution:- x1 = 101, x2 = 109 , n1 = 208, n2 = 211
  
p1 = 101/208 = 0.4856

p2 = 109/211 = 0.5166

p^ = (X1+X2)/(n1+n2) = (101+109)/(208+211) = 0.5012

q^ = 1 - 0.5011 = 0.4988

Z = (p1 -p2)/sqrt[(p^*q^*(1/n1 + 1/n2))]
= (0.4856 - 0.5166)/sqrt[ 0.5012 * 0.4988 * (1/208 + 1/211) ]
= -0.6345  

p - value = 0.2629

  

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