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

Number Sent    

Number Returned

Plain

209

102

Skydiver

218

108

Does this data support the researchers' hypothesis? Test the relevant hypotheses using = 0.10 by first calculating a P-value.

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.)

Z = _______

P-Value = _______

State the conclusion in the problem context.

Cover

Number Sent    

Number Returned

Plain

209

102

Skydiver

218

108

Explanation / Answer

Formulating the hypotheses          
Ho: p1 - p2   >=   0  
Ha: p1 - p2   <   0  
Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.488038278      
p2 = x2/n2 =    0.495412844      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.048396075      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    -0.152379433   [ANSWER, TEST STATISTIC]
  
********************************

Also, the p value is, as this is one tailed,          
          
P =    0.439443839   [ANSWER, P VALUE]

*********************************

As P > 0.10, then we    FAIL TO REJECT THE NULL HYPOTHESIS.

Hence, there is no significant evidence that that the return rate is lower for the plain cover at 0.10 level. [CONCLUSION]      

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