Question

A university official wishes to determine whether the degree of the instructor is related to the students’ opinion of the quality of instruction received. A sample of students’ evaluations of various instructors is selected, and the data in the table below are obtained. At a = 0.10, can the officials conclude that the degree of the instructor is related to the opinions of the students about the instructor’s effectiveness in the class?

	Degree of instructor
Opinion Rating	B.S.	M.S.	Ph.D.
Excellent Average Poor	14 16 3	9 5 12	4 7 16

1. Identify the appropriate test. Why do you consider this test to be the most appropriate for analyzing this study?

2. State the hypotheses.    

3. Find the critical value (s).

4. Compute the test value and the p-value.

5. Make a decision and summarize your findings.

6. Discuss any differences in the opinion rating for B.S., M.S., and Ph.D. instructors.

7. What assumptions were made in completing this test?

Answer 1

1) Here we have to test: we use chisquare test for this problem.

2)

H₀:The degree of instructor is not related to the students’ opinion of the quality of instruction received.

H₁: The degree of the instructor is related to the students’ opinion of the quality of instruction received.

3) The critical value for this test is;

X²_(4,1-0.025)= 11.14329  

4) Here I write R code for this problem.
R-code is:

x1=c(14,16,3)
x2=c(9,5,12)
x3=c(4,7,16)
d=data.frame(x1,x2,x3)
chisq.test(d)

And the output is:

> chisq.test(d)

Pearson's Chi-squared test

data: d
X-squared = 19.508, df = 4, p-value = 0.0006245

Here the value of test statistic is 19.508 and P-value is 0.0006245.

5) Here p-value is less than 0.05 thus we reject null hypothesis at 5% l.o.s.

6) And conclude that The degree of the instructor is related to the students’ opinion of the quality of instruction received.

7) It is assume that the characteristic are independent of each other.