Question

compute an interval estimate with 90% confidence for the mean time to complete an employment test. Assuming a population standard deviation of three hours, what is the required sample size if the error should be less than a half hour

Answer 1

Answer:

The required sample size 'n' = 97 .41 hours

Step-by-step explanation:

Explanation:-

Given standard deviation of the Population 'σ' = 3 hours

Given the Margin of error = $\frac{1}{2} hour$

The Margin of error is determined by

$M.E = \frac{Z_{\frac{\alpha }{2} S.D} }{\sqrt{n} }$

Given level of significance ∝ = 0.10 or 0.90

Z₀.₁₀ = 1.645

$\frac{1}{2} =\frac{1.645 X 3}{\sqrt{n} }$

Cross multiplication , we get

$\sqrt{n} = 2 X 1.645 X 3$

√n =  9.87

Squaring on both sides, we get

n = 97.41 hours

Final answer:-

The required sample size 'n' = 97.41 hours