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?

1.) Independent samples Of the course grades of students who took classes using traditional in class presentations, students to take classes online and students taught using mixed methods have been collected. The data are shown in the jpeg of the table below. Use this data to conduct the appropriate hypothesis test to determine if there is any difference between the mean scores of the student populations that took different types of classes. Use Tukey-Kramer to determine where the significant differences are.

In-Class	On-Line	Mixed
80.8	83.8	74.9
84.1	78.4	78.1
87.2	81.1	81.2
76.8	70.7	71.3
90.3	78.4	83.9
79.8	78.1	73.7
83.1	77.8	77.2

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 hypothesis being tested is:

H₀: µ₁ = µ₂ = µ₃

H_a: Not all means are equal

	Mean	n	Std. Dev
	83.16	7	4.573	In-Class
	78.33	7	4.003	On-Line
	77.19	7	4.360	Mixed
	79.56	21	4.880	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	140.651	2	70.3257	3.77	.0429
Error	335.700	18	18.6500
Total	476.351	20

The calculated value is 3.77.

The p-value is 0.0429.

Since the p-value (0.0429) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a difference between the mean scores of the student populations that took different types of classes.

Tukey simultaneous comparison t-values (d.f. = 18)
		Mixed	On-Line	In-Class
		77.19	78.33	83.16
Mixed	77.19
On-Line	78.33	0.50
In-Class	83.16	2.59	2.09
critical values for experimentwise error rate:
		0.05	2.55
		0.01	3.32

There is a significant difference between In-Class & Mixed classes.