Question

If you draw a random sample of 1000 College Students and you find that the average GPA of the students is 3.5 with a standard deviation of 0.5, what is the distribution of the average GPA? Someone argues that the average GPA of all college students is 2.5. Does your sample support that? What is your 95% CI for the population average?

Answer 1

a) Since the sample size is large, so the distribution of the sample mean is approximately normally distributed.

H₀: = 2.5

H₁: 2.5

The test statistic z = ()/()

                             = (3.5 - 2.5)/(0.5/)

                             = 63.25

At alpha = 0.05, the critical values are z_0.025 +/- 1.96

Since the test statistic value is greater than the upper critical value (63.25 > 1.96), so we should reject H₀.

So there is not sufficient evidence to support the claim that the average GPA of all college students is 2.5.

b) At 95% confidence interval the critical values are z_0.025 = 1.96

The 95% confidence interval for population mean is

+/- z_0.025 *

= 3.5 +/- 1.96 * 0.5/

= 3.5 +/- 0.031

= 3.469, 3.531