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 99% confidence level. What does the confidence interval tell about the population of all college students in the​ state?

3.8, 3.0, 4.0, 4.7, 2.9, 4.1, 3.4, 5.0, 4.8, 3.9, 4.2, 4.0, 3.4, 4.2, 3.6

What is the confidence interval for the population mean muμ​?

Answer 1

Solution:

x	x2
3.8	14.44
3	9
4	16
4.7	22.09
2.9	8.41
4.1	16.81
3.4	11.56
5	25
4.8	23.04
3.9	15.21
4.2	17.64
4	16
3.4	11.56
4.2	17.64
3.6	12.96
∑x=59	∑x2=237.36

Mean ˉx=∑xn

=3.8+3+4+4.7+2.9+4.1+3.4+5+4.8+3.9+4.2+4+3.4+4.2+3.6/15

=59/15

=3.9333

Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√237.36-(59)21514

=√237.36-232.066714

=√5.293314

=√0.3781

=0.614

Degrees of freedom = df = n - 1 = 15 - 1 = 14

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2,df = t0.005,14 =2.977

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

= 2.977 * (0.61 / 15)

= 0.47

Margin of error = 0.47

The 99% confidence interval estimate of the population mean is,

- E < < + E

3.93 - 0.47< < 3.93 + 0.47

3.46 < < 4.40

(3.46, 4.40 )