Homework SourseIt is thought that the front cover and the nature of the fir
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.
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 p1 for the plain cover and p2 for the skydiver cover.)
H0: p1 ? p2 = 0
Ha: p1 ? p2 < 0 H0: p1 ? p2 = 0
Ha: p1 ? p2 ? 0 H0: p1 ? p2 = 0
Ha: p1 ? p2 ? 0 H0: p1 ? p2 = 0
Ha: p1 ? p2 > 0
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.)
State the conclusion in the problem context.
Reject H0. The data suggests that the front cover and nature of the first question on mail surveys does influence the response rate.
Fail to reject H0. The data suggests that the front cover and nature of the first question on mail surveys does influence the response rate.
Reject H0. 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 H0. The data does not suggest that the front cover and nature of the first question on mail surveys influence the response rate.
| Cover | Number Sent | Number Returned |
|---|---|---|
| Plain | 209 | 101 |
| Skydiver | 211 | 108 |
Solution
H0: p1 ? p2 = 0
Ha: p1 ? p2 < 0
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p1=101/209 =0.4832536
p2=108/211 = 0.5118483
The test statistic is
Z=(p1-p2)/sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)
=(0.4832536-0.5118483)/sqrt(0.4832536*(1-0.4832536)/209+0.5118483*(1-0.5118483)/211)
=-0.59
It is a left-tailed test.
So the p-value= P(Z<-0.59) =0.2776 (from standard normal table)
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Fail to reject H0. The data does not suggest that the front cover and nature of the first question on mail surveys influence the response rate.
