Determine the sample size needed to construct a 99 % confidence interval to estimate the average GPA for the student population at a college with a margin of error equal to 0.7. Assume the standard deviation of the GPA for the student population is 1.0. The sample size needed is nothing. (Round up to the nearest integer.)

Answer: n = 14

Step-by-step explanation: margin of error = critical value * σ/√n

Where σ = population standard deviation = 1

n = sample size = ?

We are to construct a 99% confidence interval, hence the level of significance is 1%.

The critical value for 2 tailed test at 1% level of significance is gotten from a standard normal distribution table which is 2.58

Margin of error = 0.7

0.7 = 2.58*1/√n

0.7 = 2.58/√n

By cross multipying

0.7*√n = 2.58

By squaring both sides

0.7^2 * n = 2.58^2

0.49 * n = 6.6564

n = 6.6564/0.49

n = 14