Question

Listed below are student evaluation ratings of courses, where a rating of 5 is for excellent. The ratings were obtained at the University of Texas at Austin and it is normally distributed.

3.5 3.1 3.8 4.7 4.5 4.9 3.9 3.3 4.1 4.7 4.9 3.2 3.3 3.9 4.9 3.8 8.

Construct a 90% confidence level.

What does the confidence level tell us about the population of all college students in Texas?

Answer 1

Let the mean student evaluation rating be . Given that the population is normally distributed.

The sample is given by

Ratings(x)	x2
3.5	12.25
3.1	9.61
3.8	14.44
4.7	22.09
4.5	20.25
4.9	24.01
3.9	15.21
3.3	10.89
4.1	16.81
4.7	22.09
4.9	24.01
3.2	10.24
3.3	10.89
3.9	15.21
4.9	24.01
3.8	14.44
Total=64.5	266.45

The sample mean and sample SD are given as follows:

Now the test statistic is given by

n being the sample size; here n=16

Under the null hypothesis the test statistic follows t distribution with df=15

The critical value for 90% confidence interval, as obtained from the Biometrika table is given by

Thus the 90% confidence interval is given by

Hence the 90% confidence interval is given by

(3.548716245,4.513783755)

It can be concluded at 10% level of significance that the mean evaluation rating of courses of all the college students in Texas lies between (3.55,4.51) (approximated to 2 decimal places for the betterment of understanding).

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