Question

A student is interested in the sleep quality of students. That student selects a random sample of 21 students (age 19-24 years) from each four undergraduate years (Freshman, Sophomore, Junior and Senior), and applies Pittsburgh Sleep Quality Index (PSQI) and obtains their responses. PSQI includes 19 self-reported items and is designed to evaluate overall sleep quality (Data are presented in Table 1 below). The student is interested in determining whether there is any evidence of a difference in sleep quality across the groups of students representing each of the four different years.

1. What type of analysis should be used to answer this question? Your options are: one sample t-test, one sample z-test, Two sample t-test, chi-square, ANOVA, and paired t-test.
2. Why did you choose that type of analysis?
3. Check if the conditions for reliable use of the test are met.
4. Does the data support the hypothesis that undergraduate years are related to sleep quality PSQI score? Show any output/ graph/ chart used to answer the question.
5. Interpret your findings in context. Describe your findings as if you are interpreting it to a lay person (a person not familiar with hypothesis testing).

Table 1. Sleep quality of undergraduate students
Freshman	Sophomore	Junior	Senior
12	14	11	13
14	18	10	7
14	10	9	17
11	3	4	12
5	6	4	13
12	4	9	10
8	7	13	18
6	9	17	9
12	9	9	6
12	8	9	10
16	11	12	18
11	8	8	10
8	7	6	3
4	13	12	6
3	11	12	4
11	12	10	9
8	16	15	12
7	8	10	8
13	7	7	6
11	8	6	12
8	3	4	12

Answer 1

What type of analysis should be used to answer this question?
ANOVA

Why did you choose that type of analysis?
We need to compare the mean score for the different groups of students. This can be done using ANOVA, which check if the there is a difference in the mean of any one of the groups compared to the others.

Check if the conditions for reliable use of the test are met.
As the data is taken from the college students, we assume the following conditions are met
- Each sample is normally distributed
- Each sample is independent of the other.
- The variance of score for each group is equal.

Does the data support the hypothesis that undergraduate years are related to sleep quality PSQI score? Show any output/ graph/ chart used to answer the question.

THe steps to do ANOVA in excel are given below.
1. Put the data in excel as shown.

2. Go to Data -> data analysis - > one way anova.

3. Input the values are shown.

4. Output will be generated as follows.

Hypothesis :
Ho : the mean sleep quality for the 4 groups of students is equal.
H1 : At least one of the group has a mean sleep quality different from the other.

From the output we see that the pvalue = 0.79 (highlighted in yellow) is greater than the level of significance of 0.05, hence we fail to reject the null hypothesis and conclude that the mean sleep quality of the 4 groups is equal.