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

Answer:

Sample size minimum is 60

Step-by-step 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 = $2.58*\frac{1.5}{\sqrt{n} }$

Equate this to 0.5 and solve for n

$2.58*\frac{1.5}{\sqrt{n} }=0.5\\\sqrt{n} =7.74\\n =59.90\\n=60$