Question

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 1

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