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 _____

Answer 1

Solution :

Given that,

standard deviation = = 1.0

margin of error = E = 0.7

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Sample size = n = ((Z_/2 * ) / E)²

= ((2.576 * 1.0) / 0.7)²

= 13.5 = 14

The sample size needed is  = 14