Question

Determine the sample size needed to construct a 90​% confidence interval to estimate the average GPA for the student population at a college with a margin of error equal to 0.4. Assume the standard deviation of the GPA for the student population is 3.5

Answer 1

Solution :

Given that,

standard deviation = = 3.5

margin of error = E = 0.4

At 90% confidence level the z is ,

   = 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

Sample size = n = ((Z/2 * ) / E)2

= ((1.645 *3.5 ) /0.4 )2

= 207

Sample size = 207