9.57 An investment counselor has purchased a large mailing list consisting of 50

Question

9.57 An investment counselor has purchased a large mailing
list consisting of 50,000 potential investors. Before
creating a brochure to send to members of the list, the
counselor mails a questionnaire to a small simple random
sampling of them. In one of the questions, the respondent is
asked, “Do I think of myself as someone who enjoys taking
risks?” The response codes are (1) “Yes” and (2) “No.”
The results for the 200 investors who answered this question
are represented by the codes listed in data file XR09057.
Based on this sample, construct and interpret the 99% confidence
interval for the population proportion of investors
on the counselor’s mailing list who think of themselves as
someone who enjoys taking risks.

File XR09057:
RespCode
1
2
2
1
2
2
1
1
2
2
2
1
2
2
1
1
2
2
1
1
2
2
2
2
2
1
2
2
2
2
2
1
2
2
2
1
2
2
1
1
2
2
1
2
2
2
2
1
2
2
2
2
2
1
2
1
2
2
2
1
1
1
2
2
2
2
1
2
1
2
2
2
2
2
1
1
2
2
1
1
2
2
2
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
2
1
2
2
2
2
2
1
2
2
2
1
2
2
2
2
2
1
1
2
2
2
1
1
2
1
2
1
1
1
1
2
2
1
2
1
1
2
2
1
1
2
1
1
2
2
1
2
2
2
1
1
2
2
1
2
2
1
1
2
1
2
2
2
2
2
2
1
1
1
2
2
2
2
1
1
2
2
1
2
2
1
1
1
2
2
2
1
2
1
1
2
1
2
2
2

Explanation / Answer

n = 200, x = 80, p = 80/200 = 0.4, q = 1 - p = 0.6 Standard Error, SE = sqrt(pq/n) = sqrt(0.4 * 0.6/200) = 0.0346 (p - 2.576 * SE, p + 2.576 * SE) = (0.4 - 2.576 * 0.0346, 0.4 + 2.576 * 0.0346) = (0.3109, 0.4891)

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