Question

Listed below are student evaluation ratings of​ courses, where a rating of 5 is for​ "excellent." The ratings were obtained at one university in a state. Construct a confidence interval using a

95%

confidence level. What does the confidence interval tell about the population of all college students in the​ state?

4.1,2.8, 3.8,4.8,3.2,4.1,3.7,4.4,4.5,4.4,4.1,3.7,

3.2,4.1, 3.6

Answer 1

Here sample mean is

Create the following table.

data	data-mean	(data - mean)2
4.1	0.2	0.04
2.8	-1.1	1.21
3.8	-0.1	0.01
4.8	0.9	0.81
3.2	-0.7	0.49
4.1	0.2	0.04
3.7	-0.2	0.04
4.4	0.5	0.25
4.5	0.6	0.36
4.4	0.5	0.25
4.1	0.2	0.04
3.7	-0.2	0.04
3.2	-0.7	0.49
4.1	0.2	0.04
3.6	-0.3	0.09

Find the sum of numbers in the last column to get.

So standard deviation is

Lets assume that distribution is normal

So t value for 95% CI is TINV(0.05,14)=2.145

Hence Margin of Error is

So CI is

Hence proportion of student evaluation ratings of​ courses in the population will lie in the range of 3.597 to 4.203