Question

A research firm wants to 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? Select one: a. 196 b. 98 c. 10 d. 16

Answer 1

b. 98

Explanation:

We have that to find our
`\alpha` level, that is the subtraction of 1 by the confidence interval divided by 2. So:

`\alpha = (1-0.9)/(2) = 0.05`

Now, we have to find z in the Ztable as such z has a pvalue of
`1-\alpha`.

So it is z with a pvalue of
`1-0.05 = 0.95`, so
`z = 1.645`

Now, find M as such

`M = z*(\sigma)/(√(n))`

In which
`\sigma` is the standard deviation of the population and n is the size of the sample.

In this problem, we have that:

`M = 0.5, \sigma = 3`

`M = z*(\sigma)/(√(n))`

`0.5 = 1.645*(3)/(√(n))`

`0.5√(n) = 4.935`

`√(n) = 9.87`

`n = 97.42`

So a sample of at least 98 is required.

The correct answer is:

b. 98