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?

It is suspected that the opinions of students regarding the preferred method of teaching may be dependent upon the college in which they are enrolled. For example, students enrolled the sciences or professional schools may feel that close personal interaction with their professors is essential while students enrolled in other colleges may prefer a more independent approach to their studies.

In order to determine if student’s opinions regarding the method of teaching are independent of the college in which their major is housed, a survey of 330 students gathered data on their opinions regarding the shift to on-line studies and the colleges of their majors. The data are presented below in the Table. Use hypothesis testing to determine if the data indicates that Student Opinions are independent of College Major.

	Physical Sciences	Education	Nursing	Business and Technology	Arts and Humanities	TOTALS
Favor In-Class	11	30	14	20	55	130
Favor On-Line	20	29	9	27	33	118
Favor Mixed	19	21	7	13	22	82
TOTALS:	50	80	30	60	110	330

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.

PLEASE INCLUDE: A separate part of the answer must be a memo that answers each of the 5 questions at the top and explains why you answered as you did using the results of your statistical testing.

Answer 1

The hypothesis being tested is:

H₀: Student Opinions are independent of College Major

H_a: Student Opinions are not independent of College Major

		Physical Sciences	Education	Nursing	Business and Technology	Arts and Humanities	Total
Favor In-Class	Observed	11	30	14	20	55	130
	Expected	19.70	31.52	11.82	23.64	43.33	130.00
	O - E	-8.70	-1.52	2.18	-3.64	11.67	0.00
	(O - E)² / E	3.84	0.07	0.40	0.56	3.14	8.02
Favor On-Line	Observed	20	29	9	27	33	118
	Expected	17.88	28.61	10.73	21.45	39.33	118.00
	O - E	2.12	0.39	-1.73	5.55	-6.33	0.00
	(O - E)² / E	0.25	0.01	0.28	1.43	1.02	2.99
Favor Mixed	Observed	19	21	7	13	22	82
	Expected	12.42	19.88	7.45	14.91	27.33	82.00
	O - E	6.58	1.12	-0.45	-1.91	-5.33	0.00
	(O - E)² / E	3.48	0.06	0.03	0.24	1.04	4.86
Total	Observed	50	80	30	60	110	330
	Expected	50.00	80.00	30.00	60.00	110.00	330.00
	O - E	0.00	0.00	0.00	0.00	0.00	0.00
	(O - E)² / E	7.57	0.14	0.71	2.24	5.20	15.86
		15.86	chi-square
		8	df
		.0444	p-value

The Critical test statistic is 15.51.

The calculated value is 15.86.

The p-value is 0.0444.

Since the p-value (0.0444) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that student Opinions are not independent of College Major.

The chi-square test of independence is used here because we have two categorical variables namely faculty and favoring on-line instruction.