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):

- 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))

QUESTIONS:

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%)

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%)

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%)

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.

DATA SETS:

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

1)

The descriptive analysis of the sample of business students is obtained in excel by following these steps,

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > Descriptive Statistics > OK. The screenshot is shown below,

Step 3: Select Input range: All the the data column. Check box > Summary statistic. The screenshot is shown below,

The result is obtained. The screenshor is shown below,

The central tendency, mean and median and the sample variance are shown in blue color box above for each variable.

Now, the scatterplot for each variable is obatined in excel by following these steps,

Step 1: Write data values in excel. the screenshot is shown below,

Step 2: Select the number and Age column then INSERT > Recommended Charts > All Charts > Scatter with Straight Lines and Markers > OK.

The Chart is obtained, The screenshot is shown below,

Similarly the chart is obatined for other variables. The screenshots are shown below,

The scatter plot between age and Satifaction for stage 1 and stage 2 is shown below,

.

2)

Two sample t test is used to compare the means assuming equal variance in excel by following these steps,

Step 1: Write the data value in excel.

Step 2: DATA > Data Analysis > Two Sample t test: Assuming equal varince. The screenshot is shown below,

Step 3: Select Variable 1 Range: stage 1, Variable 2 Range: stage 2 column, Hypothesized mean difference: 0, enter Alpha: 0.05. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

The corresponding P-value is 0.0385 which is less than 0.05 at the 5% significance level for the one sided alternative hypothesis. Hence, it can be concluded that the null hypothesis is rejected.

Now, it can be concluded that there is statistically significant difference between two stage of satisfaction.

3)

From the result summary obtained above, the confidence interval can be obtained using the formula,

4)

A single factor ANOVA is used in excel to test the null hypothesis that all the means are equal. The hypothesis is defined as,

Null Hypothesis:

Alternative hypothesis; All the means are not equal.

The test is perfomed in excel by using following steps,

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > ANOVA: Single Factor > OK.  The screenshot is shown below,

Step 3: Select Input Range: All the data values column. The screenshot is shown below,

The result is obtained.  The screenshot is shown below,

From the result summary,

The P-value is greater than 0.05 at 5% significance level hence the null hypothesis can not be rejected. Now, we can state that there is no statistically significant difference among means at 5% significance level.