Question

Suppose you sample 12 UIUC students and record their GPAs in order to estimate the average GPA of all students on campus. The data you collected are shown below. Since sample size is small, you will analyze your data using the t-distribution.

3.8 3.1

2.5 3.3

2.6 2.9

2.9 3

1.6 2.8

2.7 2.3

a. What is the 95% confidence for the true population mean? Include an interpretation of your confidence interval. b. What distribution does a t-distribution approach as sample size increases?

Answer 1

a)

sample mean         x=	2.792
sample size             n=	12.00
sample std deviation s=	0.542
std error sx=s/√n=	0.1564

for 95% CI; and 11 df, critical t=		2.2010
margin of error E=t*std error                            =		0.344
lower bound=sample mean-E =		2.45
Upper bound=sample mean+E=		3.14
from above 95% confidence interval for population mean =(2.45,3.14)

Interpreation: above interval gives 95% confidence to contain true value of population mean

b)

as sample size incerases   a t-distribution approach standard normal(z) distribution