Question

you want to create a 99 confidence interval with a margin of error of 25 assuming that the population standard deviation is equal to 1.5 what's the minimum size of the Rams Tampa

Answer 1

The minimum sample size is 239.

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 Z-table as such z has a p-value of
`1 - \alpha`.

That 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.

Population standard deviation is equal to 1.5

This means that
`\sigma = 1.5`

Margin of error of 0.25

This means that
`M = 0.25`

What's the minimum size of the sample?

`M = z(\sigma)/(√(n))`

`0.25 = 2.575(1.5)/(√(n))`

`0.25√(n) = 2.575*1.5`

`√(n) = (2.575*1.5)/(0.25)`

`(√(n))^2 = ((2.575*1.5)/(0.25))^2`

`n = 238.7`

Rounding up:

The minimum sample size is 239.