Question

A school board wishes to know the current mean reading level of 6th graders throughout a very large school district. Past experience shows that the standard deviation of such reading scores is about 2.5. If they wish to be 95% sure that their result is correct to within .4, how large a sample do they need to have?

Answer 1

Sample size should be atleast 60025

Explanation:

Given that a school board wishes to know the current mean reading level of 6th graders throughout a very large school district. Past experience shows that the standard deviation of such reading scores is about 2.5

For 95% confidence we have significance level = 5%

Margin of error = 0.04

Margin of error should be less than 0.04

i.e. Z critical value for 95% *std error <0.04

`1.96*(2.5)/(√(n) ) <0.02\\\\n>60025`

Sample size should be atleast 60025