Question

The following data set contains the college GPA of a sample of ten randomly selected UWG professors:

1.8, 2.1, 2.3, 2.5, 2.6, 3.2, 3.4, 3.7, 3.9, 4

A.) Construct a normal probability plot of the data set. Do the GPA’s appear to be normally distributed? Yes or No.

B.) Find the critical t value that corresponds to a 90% confidence level for the data rounded to 2 decimal places.

C.) Construct a 90% confidence interval for the mean GPA of the professors, round answers to 2 decimal places.

Answer 1

A) By using R software we can construct the normal probability plot of the data set.

First, enter data into R software.

R codes and output.

data<-c(1.8,2.1,2.3,2.5,2.6,3.2,3.4,3.7,3.9,4)
qqnorm(data)

Yes, the GPA’s appear to be normally distributed.

B)

Sample size = n = 10

Degrees of freedom = n - 1 = 10 - 1 = 9

Level of significance = 0.10

Critical value = 1.83    ( Using t table)

C) We have to construct a 90% confidence interval for the mean GPA of the professors.

Sample mean = = 2.95

Standard deviation = s = 0.7906

Formula is

Here E is a margin of error.

So confidence interval is ( 2.95 - 0.4575 , 2.95 + 0.4575) = > ( 2.49 , 3.41)