Question

8.3.57 Question Help A survey of 437 women revealed that 49% wear flat shoes to work. a. Use this sample information to develop a 95% confidence interval for the population proportion of women who wear flat shoes to work. b. Suppose that the people who administered this survey now wish to estimate the proportion of women who wear athletic shoes to work with a margin of error of 0.01 with 99% confidence. Determine the sample size required. 1 sps (Round to three decimal places as needed.) 10 a

Answer 1

Solution-A:

z crit for 95%=1.96

n=437

p^=0.49

95% confidence interval for p

p^-z*sqrt(p^*(1-p^)/n),p^+z*sqrt(p^*(1-p^)/n)

0.49-1.96*sqrt(0.49*(1-0.49)/437),0.49+1.96*sqrt(0.49*(1-0.49)/437)

0.4431296,0.5368704

0.443<p<0.537

answer:

0.443<p<0.537

Solution-b:

with prior estimate =0.49

z crit for 99%=2.576

E=margin of error=0.01

n=(Z/E)^2*p*(1-p)

=(2.576/0.01)^2*0.49*(1-0.49)

= 16582.8

=16583

ANSWER:

n=16583