Question

In 2010, an online security firm estimated that 67% of computer users don't change their passwords very often. Because this estimate may be outdated, suppose that you want to carry out a new survey to estimate the proportion of students at your school who do not change their password. You would like to determine the sample size required to estimate this proportion to within a margin of error of 0.03 with 95% confidence.

(a)Using 0.67 as a preliminary estimate for the proportion, what is the required sample size if you want to estimate this proportion with a margin of error of 0.03? (Give your answer as a whole number.)

(b)Calculate the required sample size if no preliminary estimate for the proportion is used. (Give your answer as a whole number.)

Answer 1

solution:

Given data:

Given that, estimate of population proportion = p = 0.67

margin of error (E) = 0.03

A 95% confidence level has significance level of 0.05 and critical value is,

We want to find the sample sizes for the following cases :

a)

If we used a preliminary estimate of 0.67 then,

Therefore, n ≥ 944

b)

If we don't used the preliminary estimate then,

Therefore, n ≥ 1068

Note : if you want sample size is to nearest whole number then, n ≥ 1067

please give me thumb up