Question

eCampusOntario.ca is the primary face of the Ontario Online Learning Consortium (OOLC), a not-for-profit corporation whose membership is composed of all publicly-funded colleges and universities in Ontario. Funding for OOLC and the eCampusOntario initiative comes from the Government of Ontario.

eCampusOntario.ca was created in 2015 primarily as a portal for learners to find online courses– through browsing, searching by keyword, or filtering by institution and delivery format. Course details include links to information about scheduling, tuition and fees, instructors, and information about how to get registered and to seek credit transfer. Previously identified course equivalencies are also listed where available. In addition, students can search based on a specific course they need credit for to find available online options at other institutions.

Aiming to improve its services, eCampusOntario has collected data from 33 nursing students, 33 business students and 33 education students on their satisfaction with the eCampusOntario portal prior to registration for any courses (stage 1) and after registration (stage 2). The following information is available for each stream (refer to data sheet):

1.

- - -

-

age of the respondents
gender (1=male and 2=female)
Student satisfaction of stage 1 (ranges from 1 (extremely dissatisfied) to 5 (extremely satisfied))
Student satisfaction of stage 2 (ranges from 1 (extremely dissatisfied) to 5 (extremely satisfied))

Question 1)

Conduct a descriptive analysis of the sample of business students which includes the following:

measures of central location and variance/covariance for the relevant variables

represent each variable graphically using one of the types of graphs discussed in

the course

represent any relevant relationships between the variables using appropriate

graphs (20%)

Question 2)

Some eCampusOntario employees believe more information is provided to business students during stage 1 than during stage 2. Is there evidence to suggest that the satisfaction level of business students is higher for stage 1 than for stage 2? (25%)

Question 3)

Estimate the difference between the satisfaction level of business students during stage 1 and during stage 2 with 95% confidence. Explain what the result means in your own words. (20%)

Quesiton 4)

eCampusOntario would also like to know if differences exist between the satisfaction levels of nursing students, business students and education students during stage 2. Do differences exist? Assume the variables have equal variance. (30%)

* assume a significance level of .05 for all hypotheses being tested.

Directions:

Answer each question on a separate Excel Sheet and include all Excel results.

For each question do the following:

State your chosen method of analysis and justify its use. If the question involves testing a hypothesis, state the hypotheses.

State the required conditions for all tests performed and whether they are satisfied, justifying your answer with any necessary analysis.

Briefly discuss how the findings can help eCampusOntario in future decision making.

Business
Age	Gender	Business-Student Satisfaction of Stage 1	Business- Student Satisfaction of Stage 2
18	1	3.02	2.83
18	2	3.60	3.11
19	2	2.88	1.87
19	1	3.70	3.82
19	2	4.41	4.00
20	2	2.95	2.72
21	1	4.39	4.39
22	2	3.00	2.00
22	2	3.11	2.91
22	2	3.75	2.90
22	1	4.47	4.00
23	2	2.81	2.80
23	1	3.13	2.50
23	1	3.71	3.34
23	1	4.50	4.22
24	2	1.00	0.50
24	2	3.23	2.77
25	1	3.74	3.71
26	2	3.52	3.52
26	1	3.58	3.71
26	1	3.79	2.90
27	2	1.38	1.00
27	2	4.48	4.00
30	1	2.76	2.48
30	1	3.50	3.11
31	2	3.10	2.98
32	2	3.46	3.22
33	1	4.35	4.29
37	2	3.78	3.12
38	1	2.83	2.00
43	2	2.86	1.50
51	2	3.57	3.22
52	1	1.30	0.50

Nursing
Age	Gender	Nursing-Student Satisfaction of Stage 1	Nursing-Student Satisfaction of Stage 2
19	1	1.52	2.22
19	1	2.10	2.80
20	1	1.38	2.08
20	1	2.20	2.90
20	2	2.91	3.61
21	2	1.45	2.15
22	2	2.89	3.59
23	2	1.50	2.20
23	1	1.61	2.31
23	2	2.25	2.95
23	1	2.97	3.67
24	2	1.31	2.01
24	1	1.63	2.33
24	2	2.21	2.91
24	2	3.00	3.70
25	1	0.30	1.00
25	1	1.73	2.43
26	1	2.24	2.94
27	2	2.02	2.72
27	2	2.08	2.78
27	2	2.29	2.99
28	1	0.50	1.20
28	2	2.98	3.68
31	1	1.26	1.96
31	2	2.00	2.70
32	1	1.60	2.30
33	2	1.96	2.66
34	2	2.85	3.55
38	2	2.28	2.98
39	1	1.33	2.03
44	1	1.36	2.06
52	1	2.07	2.77
53	1	0.50	1.20

Education
Age	Gender	Education-Student Satisfaction of Stage 1	Education-Student Satisfaction of Stage 2
18	1	2.52	2.63
18	1	3.10	3.22
18	2	2.38	2.45
18	1	3.20	3.02
19	2	3.91	4.55
19	1	2.45	2.87
19	2	3.89	4.00
19	2	2.50	2.35
20	1	2.61	2.49
20	2	3.25	2.75
20	1	3.97	4.21
21	1	2.31	2.15
21	1	2.63	2.64
21	1	3.21	3.25
22	2	4.00	4.00
22	2	0.50	0.50
24	2	2.73	2.46
25	1	3.24	3.46
25	2	3.02	3.25
27	1	3.08	3.59
28	2	3.29	3.00
29	1	1.50	1.50
29	2	3.98	4.00
32	1	2.26	2.00
32	2	3.00	3.42
33	1	2.60	2.75
34	2	2.96	2.51
35	2	3.85	3.58
39	2	3.28	3.26
40	1	2.33	2.55
45	1	2.36	2.88
53	2	3.07	3.05
54	2	1.50	1.00

Answer 1

(first part) Are there evidence to suggest there are significant differences between the business student’s satisfactions of the two stages. (30%)

(answer of first part)

		stage1	stage2
mean		3.32	2.36
s		0.86	0.78
n		33	33

here we use t-test with null hypothesis H0:mean1=mean2 and alternate hypothesis H1:mean1?mean2

t=(mean1-mean2)/((s_p*(1/n1 +1/n2)^1/2) and s_p²=((n1-1)s1²+(n2-1)s2²)/n and with df is n=n1+n2-2

since p-value is less than alpha=0.05, so we reject H0 and conclude that there is significant difference between stage1 and stage2. for business

t-test
	sample	mean	s	s2	n	(n-1)s2
	stage1	3.32	0.86	0.7396	33	23.6672
	stage2	2.36	0.78	0.6084	33	19.4688
	difference=	0.96		1.348	66	43.136
	sp2=	0.674
	sp=	0.8210
	t=	4.7499
one tailed	p-value=	0.000006
two tailed	p-value=	0.000012

(second part) Estimate the difference between business student satisfaction during stage 1 and 2 with 95% confidence. Interpret the results. (20%)

(answer of second part) difference between business student satisfaction=3,32-2.36=0.96

(third part) eCampusOntario would also like to know if differences exist between student satisfaction of nursing, business and education during stage 2. Assume variable have equal variance. (30%)

(answer of third part) here we want test equality of more than two sample means ( nursing, business and education). one way anova will be used to test the

null hypothesis H0:1=2=3

alternate hypothessis H1: at least one mean is different from another, since data of education is not available, it is difficult to answer without this.

Assume significance level of .05 when needed.