Question

A researcher wants to estimate the mean age of all Business Week readers at a 99% confidence level. The standard deviation of ages of all Business Week readors is nine years. The sample size that will yield a maximum error of estimate within three years of the population mean is at least:

A. 60
B. 97
C. 185
D. 8

Answer 1

A. 60

Explanation:

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

`\alpha = (1-0.99)/(2) = 0.005`

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
`1-0.005 = 0.995`, so
`z = 2.575`

Now, find the margin of error 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.

We have to find:

n when
`M = 3, \sigma = 9`. So

`M = z*(\sigma)/(√(n))`

`3 = 2.575*(9)/(√(n))`

`3√(n) = 9*2.575`

Dividing both sides by 3

`√(n) = 3*2.575`

`(√(n))^(2) = (3*2.575)^(2)`

`n = 59.68`

We round up, so the correct answer is:

A. 60