Question

How large a sample should be selected to provide a 95 confidence interval with a margin of error of 10? Assume that the population standard deviation is 40.

Answer 1

the required sample size is 62

Explanation:

Given the data in the question;

Confidence interval C = 95% = 0.95

Margin of error E = 10

population standard deviation σ = 40

sample size n = ?

We use the following formula to get our sample size;

sample size n = ( (
`Z_c` × σ ) / E )²

Next we find z value for confidence interval

Confidence interval C = 95% = 0.95

Area = ( 1 + c )/2 = ( 1 + 0.95)/2 = 1.95 / 2 = 0.975

Now we check our z-table to see the area where 0.975 falls;

It falls under column 0.06 and Row 1.9

so, our z-value for confidence interval of 0.95 is 1.96

so we substitute

sample size n = ( ( 1.96 × 40 ) / 10 )²

n = ( 78.4 / 10 )²

n = ( 7.84 )²

n = 61.4656

we know that sample size is always rounded up, so

n = 62

Therefore, the required sample size is 62