Question

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

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 p̂ will be within a distance of 0.03 from p? (Round your answer up to the nearest whole number.)
_____ students

(b) A report indicates that approximately 54% of college students are females. Answer part (a) using this estimate for p. (Round your answer up to the nearest whole number.)
______ students

Answer 1

Solution :

Given that,

= 0.5 ( assume 0.5)

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.03

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.58    ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (2.58 / 0.03)2 * 0.5 * 0.5

=1849

Sample size = 1849

(B)

Solution :

Given that,

= 0.54

1 - = 1 - 0.54 = 0.46

margin of error = E = 0.03

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.58    ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (2.58 / 0.03)2 * 0.54 * 0.46

=1837.16

Sample size = 1837