Question

7) In a recent Pew Research Center survey (Oct 17, 2019) of 3500 U.S. adults, 1890 adults said congress should continue with impeachment proceedings. 18 points a) Show work for finding the point estimate, p b) Find the margin of error, E, using a 95% confidence level and round to 3 decimal places. c) Find a 95% confidence interval for the population proportion from this survey, show all values used and round to 3 decimals. d) Interpret your answer. e) Find the minimum sample size required to find a 95% confidence interval estimate for a population proportion if you want a margin of error of 3% with no preliminary estimate.

Answer 1

7) a)$\large \widehat{p}=\frac{1890}{3500}=0.54$

b) z value for 95% CI is 1.96 as P(-1.96<z<1.96)=0.95

So Margin of Error is

E = Z* V ñ pq = 1.96* V 0.54 * 0.46 P = 0.017 3500

c. Hence CI is $\large p \pm E=0.54 \pm 0.017=(0.523,0.557)$

d. Population proportion will lie in the range of 0.523 to 0.557

e. Here E=0.03

So $\large n=(\frac{z}{E})^2*p*q=(\frac{1.96}{0.03})^2*0.54*0.46=1060.28=1061$