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?

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.

The question among of many administrators concerns the willingness of the faculty to embrace the use of on-line or mixed methods of instruction. Many of the faculty deeply believe that there is no substitute for face-to-face contact with students. They maintain that instructors get a better sense of student’s understanding of the course material when they can see them.

In order to gauge the attitudes of instructors, faculty from five of the university Colleges have been asked whether they favor or do not favor using on-line or mixed instructional methods. The data are shown in the Table below.

	Physical Sciences	Education	Nursing	Business and Technology	Arts and Humanities	TOTALS
Favor On-Line Or Mixed	35	40	19	23	36	153
Don't Favor On-Line or Mixed	95	50	51	27	24	247
TOTALS:	130	90	70	56	60	400

Use hypothesis testing to determine if the proportion of faculty favoring on-line instruction is equal for all of the university’s Colleges.

Answer 1

The hypothesis being tested is:

H₀: The proportion of faculty favoring on-line instruction is equal for all of the university’s Colleges

H_a: The proportion of faculty favoring on-line instruction is not equal for all of the university’s Colleges

		Physical Sciences	Education	Nursing	Business and Technology	Arts and Humanities	Total
Favor On-Line Or Mixed	Observed	35	40	19	23	36	153
	Expected	49.73	34.43	26.78	19.13	22.95	153.00
	O - E	-14.73	5.58	-7.78	3.88	13.05	0.00
	(O - E)² / E	4.36	0.90	2.26	0.79	7.42	15.73
Don't Favor On-Line or Mixed	Observed	95	50	51	27	24	247
	Expected	80.28	55.58	43.23	30.88	37.05	247.00
	O - E	14.73	-5.58	7.78	-3.88	-13.05	0.00
	(O - E)² / E	2.70	0.56	1.40	0.49	4.60	9.74
Total	Observed	130	90	70	50	60	400
	Expected	130.00	90.00	70.00	50.00	60.00	400.00
	O - E	0.00	0.00	0.00	0.00	0.00	0.00
	(O - E)² / E	7.06	1.46	3.66	1.27	12.02	25.47
		9.49	critical value
		25.47	chi-square
		4	df
		4.05E-05	p-value

The Critical test statistic is 9.49.

The calculated value is 25.47.

The p-value is 0.000.

Since the p-value (0.000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the proportion of faculty favoring on-line instruction is not equal for all of the university’s Colleges.

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