9.-10 points MBasicStat7 22. E.033. My Notes You are planning a survey of studen

Question

9.-10 points MBasicStat7 22. E.033. My Notes You are planning a survey of students at a large university to determine what proportion favor an increase in student fees to support an expansion of the student newspaper. Using records provided by the registrar, you can select a random sample of students. You will ask each student in the sample whether he or she is in favor of the proposed increase. Your budget will allow a sample of 200 students. (Round your answers to four decimal places.) (a) For a sample of size 200, construct a table of the margins of error for 95% confidence intervals when p takes the values 0.1, 0.3, 0.5, 0.7, and 0.9 0.3 0.5 0.7 0.9 (b) A former editor of the student newspaper offers to provide funds for a sample of size 550. Repeat the margin of error calculations in part (a) for the larger sample size m.e. 0.3 0.5 0.7 0.9 You may need to use the appropriate Appendix Table to answer this question eBook

Explanation / Answer

Margin of error = z *sqrt(pq/n)

for 95 % confidence interval

z = 1.96

for n = 200

for n = 550

16 out of 16 has cocaine traces so

add 2 success and 2 failure

so p=(16+2)/(16+4)=0.9

p+-z*sqrtr((p*(1-p))/(n+4))=(0.9-1.96*sqrt(0.9*0.1/20), (0.9+1.96*sqrt(0.9*0.1/20)

=(0.768519, 1.0314807)

RHS should be 1 as p can never be more than 1

p margin of error 0.1 0.041577879 0.3 0.063511259 0.5 0.069296465 0.7 0.063511259 0.9 0.041577879

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