Question

As you might expect, there has been a spirited discussion about which method is most effective in terms of the effectiveness of delivering course content, student and faculty acceptance of different modes of instruction and the cost to the state of using different delivery methods. As a result of this discussion, five questions have arisen that require the use of statistics to answer them. They are:

1. Does student learning as indicated by average grades suffer if they are taught using alternative modes of instruction: traditional in-class teaching, on-line learning, or mixed on-line/in-class method?

2. Do students have a preference for which type of learning to which they are exposed?

3. Is the acceptance of students of on-line methods independent of their majors?

4. Is the proportion of faculty members favoring on-line or mixed delivery the same for all colleges within the university?

5. Does the average amount of additional instructor time required to deliver courses on-line differ according to the type of courses?

- In order to determine which type of instruction students prefer, the university surveyed 620 students studying at Tennessee universities who have been exposed to different types of instruction. The results are shown in the Table below:

Student Preference	In-Class	On-Line	Mixed	Total
Prefer	100	105	115	320
Do Not prefer	100	115	85	300
TOTAL	200	220	200	620

Please provide a statistical analysis. You are required to submit the following information:

1.) The null and alternative hypotheses being tested.

2.) The Critical test statistic (F or Chi-Square) from the appropriate table. If it required using the Tukey- Kramer method, show the Q score from the table AND the critical value that you used to make your decisions. Also, specify which mean or means are not equal.

3.) The calculated value that you arrived at and the p-Value.

4.) Your decision, reject or do not reject.

5.) A separate part of the answer must be a memo sheet written in word that answers each of the 5 questions and explains why you answered as you did using the results of your statistical testing.

Answer 1

The Chi-square method is used because we have two categorical variables here.

The hypothesis being tested is:

H₀: There is no preference in the type of instruction among students studying at Tennessee universities who have been exposed to different types of instruction

H_a: There is a preference in the type of instruction among students studying at Tennessee universities who have been exposed to different types of instruction

The Critical test statistic is 5.991.

The calculated value is 4.31.

The p-value is 0.1157.

Since the p-value (0.1157) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is a preference in the type of instruction among students studying at Tennessee universities who have been exposed to different types of instruction.

		In-Class	On-Line	Mixed	Total
Prefer	Observed	100	105	115	320
	Expected	103.23	113.55	103.23	320.00
	O - E	-3.23	-8.55	11.77	0.00
	(O - E)² / E	0.10	0.64	1.34	2.09
Do Not prefer	Observed	100	115	85	300
	Expected	96.77	106.45	96.77	300.00
	O - E	3.23	8.55	-11.77	0.00
	(O - E)² / E	0.11	0.69	1.43	2.23
Total	Observed	200	220	200	620
	Expected	200.00	220.00	200.00	620.00
	O - E	0.00	0.00	0.00	0.00
	(O - E)² / E	0.21	1.33	2.78	4.31
		5.991	critical value
		4.31	chi-square
		2	df
		.1157	p-value