Question

Suppose that scores on the mathematics part of the National Assessment of Educational Progress (NAEP) test for eighth-grade students follow a Normal distribution with standard deviation σ = 110 . You want to estimate the mean score within ± 10 with 90 % confidence. How large an SRS of scores must you choose? Give your answer as a whole number.

Answer 1

A sample size of at least 328 students is required.

Explanation:

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

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find the width M as such

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

In this problem, we have that:

So:

A sample size of at least 328 students is required.

Answer 2

A sample size of at least 328 students is required.

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 the width 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 = 10, \sigma = 110`

So:

`M = z*(\sigma)/(√(n))`

`10 = 1.645*(110)/(√(n))`

`10√(n) = 180.95`

`√(n) = 18.095`

`n = 327.43`

A sample size of at least 328 students is required.