Question

You want to create a 99% confidence interval with a margin of error of .5. Assuming the population standard deviation is equal to 1.5, what's the minimum size of the random sample you can use for this purpose?

Answer 1

Sample size minimum is 60

Explanation:

given that you want to create a 99% confidence interval with a margin of error of .5.

The population standard deviation is equal to 1.5

i.e.
`\sigma = 0.5`

Confidence level = 99%

Since population std deviation is known, we can use Z critical value for finding margin of error

Z critical value for 99% = 2.58

Margin of error =
`2.58*(1.5)/(√(n) )`

Equate this to 0.5 and solve for n

`2.58*(1.5)/(√(n) )=0.5\\√(n) =7.74\\n =59.90\\n=60`