Question

What percentage of your campus student body is female? Let p be the proportion of women students on your campus.

(a) If no preliminary study is made to estimate p, how large a sample is needed to be 99% sure that a point estimate p^ will be within a distance of 0.05 from p?

(b) A report indicates that approximately 57% of college students are female. Answer part (a) using this estimate for p.

Answer 1

a) No preliminary study is made to estimate p.

So consider p = 0.5

Margin of error = E = 0.05

confidence level = c = 0.99

z critical value for (1+c)/2 = (1+0.99)/2 is

zc = 2.58             (From statistical table of z values)

Sample size (n) :

n = 665.64

n = 666               (Round to nearest integer)

Sample size = 666

b) .

p = 0.57

Margin of error = E = 0.05

confidence level = c = 0.99

z critical value for (1+c)/2 = (1+0.99)/2 is

zc = 2.58             (From statistical table of z values)

Sample size (n) :

n = 652.5935

n = 653             (Round to nearest integer)

Sample size = 653