Question

Suppose you are constructing a 95% confidence interval for the mean of a single sample, whose population standard deviation is known to be σ = 5. You calculate the sample size with some specified width (error) E.

(a) Reducing your confidence level to 80%, and reducing your original width (error) E by a third ( 1 3 ), how much bigger will the new sample size be compared to the first sample size above? (Hint: find the scaled size using algebra).

b) Suppose instead that your increase the sample size by a factor of 10 and you allow the confidence level to be 85%, how will the width (error) have scaled in size compared to the original width (error) E?

Answer 1