Question

The population standard deviation for the scores of a standardized test is 5 points. If we want to be 95% confident that the sample mean is within 2 points of the true population mean, what is the minimum sample size that should be taken

Answer 1

The answer is 25. You should round up not down

Explanation:

Answer 2

The minimum sample size that should be taken is 24.

Explanation:

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

`\alpha = (1-0.95)/(2) = 0.025`

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
`1-0.025 = 0.975`, so
`z = 1.96`

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.

If we want to be 95% confident that the sample mean is within 2 points of the true population mean, what is the minimum sample size that should be taken

This is n when
`M = 2, \sigma = 5`

`M = z*(\sigma)/(√(n))`

`2 = 1.96*(5)/(√(n))`

`2√(n) = 1.96*5`

`√(n) = (1.96*5)/(2)`

`(√(n))^(2) = ((1.96*5)/(2))^(2)`

`n = 24.01`

The minimum sample size that should be taken is 24.