Question

4. First-semester GPAs of a random selection of 40 freshmen at a large university are found to have a mean of 2.72. The standard deviation for the sample is found to be s = 0.62. Estimate the true mean GPA of the entire freshman class with 90% confidence.

We can be 90% confident that the true mean of the freshman class is between _______ and ______________.

Answer 1

4)

Solution :

Given that,

Point estimate = sample mean = = 2.72

sample standard deviation = s = 0.62

sample size = n = 40

Degrees of freedom = df = n - 1 = 39

t _/2,df = 1.685

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

= 1.685 * (0.62 / 40)

Margin of error = E = 0.17

The 90% confidence interval estimate of the population mean is,

- E < < + E

2.72 - 0.17 < < 2.72 + 0.17

2.55 < < 2.89

We can be 90% confident that the true mean of the freshman class is between 2.55 and 2.89 .