Question

The population standard deviation for the temperature of beers found in Scooter's Tavern is 0.26 degrees. If we want to be 90% confident that the sample mean beer temperature is within 0.1 degrees of the true mean temperature, how many beers must we sample

Answer 1

19 beers must be sampled.

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

That is z with a pvalue of
`1 - 0.05 = 0.95`, so Z = 1.645.

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.

The population standard deviation for the temperature of beers found in Scooter's Tavern is 0.26 degrees.

This means that
`\sigma = 0.26`

If we want to be 90% confident that the sample mean beer temperature is within 0.1 degrees of the true mean temperature, how many beers must we sample?

This is n for which M = 0.1. So

`M = z(\sigma)/(√(n))`

`0.1 = 1.645(0.26)/(√(n))`

`0.1√(n) = 1.645*0.26`

`√(n) = (1.645*0.26)/(0.1)`

`(√(n))^2 = ((1.645*0.26)/(0.1))^2`

`n = 18.3`

Rounding up:

19 beers must be sampled.