Topic A: How has COVID influenced university enrollment in Fall 2022?
The rumor says that the university enrollment in the U.S. has been negatively impacted by COVID. To better understand whether this speculation is true, a research team collected enrollment data from 10 universities across the nation. The research team is going to do some formal statistical analyses based on this sample.
Here are the enrollment data the research team collected:
|
Enrollment in 2020 (pre COVID)
|
Enrollment in 2021 (post COVID)
|
University #1
|
5,034
|
3,452
|
University #2
|
1,223
|
1,101
|
University #3
|
2,948
|
3,210
|
University #4
|
3,542
|
3,412
|
University #5
|
1,652
|
1,291
|
University #6
|
4,982
|
4,568
|
University #7
|
6,392
|
6,016
|
University #8
|
2,372
|
2,156
|
University #9
|
3,962
|
3,621
|
University #10
|
4,127
|
4,321
|
1)
Please state the null hypothesis and the alternative hypothesis.
2)
Please compute the mean differences and their standard deviation:
Mean for Enrollment in 2020: 36,234/10=3623.4
Mean for Enrollment in in 2021: 33,148/10=3314.8
Mean Differences: 3623.4 – 3314.8 =308.6
Standard Deviation for 2020: (I used the excel function Stdev.S) =1617.48
Standard Deviation for 2021: (I used the excel function Stdev.S) =1503.77
3)
What is the t value of this test? Please demonstrate the computation steps.
4)
What is the statistical conclusion you draw from this test? Please explain why.
5)
What is the managerial/practical conclusion you draw from this test?
Topic B: Selecting the Best Music for a Local Coffee Shop
A local coffee shop is looking for new background music for its customers. After brainstorming for a few days, the shop owner narrowed it down to three options: classical music, jazz, and soft rock.
The shop owner recruited 24 target customers, and randomly assigned them to listen to one of the three options while they were in the shop. Each customer rated how much they liked the music on a 7-point scale. The collected data is shown below:
Participant ID
|
Classical Music
|
Participant ID
|
Jazz
|
Participant ID
|
Soft Rock
|
1
|
6
|
9
|
1
|
17
|
2
|
2
|
2
|
10
|
7
|
18
|
3
|
3
|
4
|
11
|
6
|
19
|
4
|
4
|
5
|
12
|
5
|
20
|
1
|
5
|
6
|
13
|
5
|
21
|
2
|
6
|
6
|
14
|
4
|
22
|
3
|
7
|
3
|
15
|
6
|
23
|
2
|
8
|
4
|
16
|
7
|
24
|
2
|
Mean
|
4.50
|
|
5.13
|
|
2.38
|
SD
|
1.51
|
|
1.96
|
|
0.92
|
6)
State the null and the alternative hypotheses in the context of the problem.
7)
Complete the ANOVA Table below (please also show your calculation steps below the table):
Source of Variation
|
Sum of Square (SS)
|
D.F
|
Mean Square (MS)
|
F-Value
|
Between-Group
|
33.25
|
|
16.63
|
|
Within Group
|
|
21
|
|
|
Total
|
|
|
|
|
8)
Given the findings from the ANOVA table, provide the statistical conclusion for this problem.
9)
Based on your findings, which music option should the shop owner choose to play in the coffee shop? (Assume the least significant difference [LSD] is 1.59).