Answer to Question #175746 in Statistics and Probability for Ajay Singh

Question

1.      The head of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option. A preliminary sample indicates that the proportion will be around 0.25. Therefore, what size sample should the department head take if she wants to be 95% confident that the estimate is within 0.10 of the true proportion? (1)

Answer 1

Margin of error E = 0.10

Significance level α = 0.05

The critical value

$Z_{α/2}=Z_{0.05/2}=1.96$

The Excel function is

=NORMSINV(0.05/2)

Since, the estimate of the population proportion is known.

$\hat{p}=0.25$

Therefore, the required sample size is

$n = \hat{p}(1- \hat{p}) (\frac{Z_{α/2}}{E})^2 \\ = 0.25(1 – 0.25)(\frac{1.96}{0.10})^2 \\ = 72$