Question

You draw a random sample of 626 Fort Hays State students and measure their Grade Point Average. The mean GPA of the sample is 3.0, with a standard deviation of .5. What would be the 95% confidence interval for the GPA of the population of all Fort Hays State students.

		2.759 to 3.241
		2.815 to 3.185
		2.881 to 3.119
		2.96 to 3.04

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 3.0

sample standard deviation = s = 0.5

sample size = n = 626

Degrees of freedom = df = n - 1 = 626 - 1 = 625

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

t/2,df = 1.964

Margin of error = E = t/2,df * (s /n)

= 1.964 * (0.5 / 626)

Margin of error = E = 0.04

The 95% confidence interval estimate of the population mean is,

  ± E

3.0 ± 0.04

(2.96 , 3.04)