Question

A researcher is interested in estimating the mean time it takes adults to learn a certain task. He wants to be 90% confident that the mean time for a sample of adults is within 1.8 minutes of u. In a small pilot study the standard deviation of learning times was 6.5 minutes. How large a sample of adults should be tested? Round the critical value to three decimal places.

Answer 1

Solution :

Given that,

standard deviation = $\sigma$ = 6.5

margin of error = E = 1.8

At 90% confidence level the z is ,

$\alpha$ = 1 - 90% = 1 - 0.90 = 0.10

$\alpha$ / 2 = 0.10 / 2 = 0.05

Z_$\alpha$/2 = Z_0.05 = 1.645

The critical value = 1.645

Sample size = n = ((Z_$\alpha$/2 * $\sigma$ ) / E)²

= ((1.645 * 6.5) / 1.8)²

= 35.28

= 35

Sample size = 35