Question

In: Statistics and Probability

The head of a computer science department is interested in estimating the proportion of students entering...

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 0.208.

What size sample should the department head take if she wants to be 95% confident that the estimate is within 0.02 of the true proportion?

Expert Solution

Solution :

Given that,

= 0.208

1 - = 1 - 0.208 = 0.792

margin of error = E = 0.02

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

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

= (1.96 / 0.02)2 * 0.208 * 0.792

= 1582.12

Sample size =1582

orchestra answered 2 years ago

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