Gender	Alcohol	Exercise	SQI	GPA
Male	Yes	9	15.5	3.85
Male	Yes	11	11.0	5.46
Female	No	5	11.1	3.28
Female	No	6	13.9	2.37
Female	Yes	8	9.9	4.63
Male	Yes	11	14.5	4.58
Male	Yes	9	10.6	4.96
Male	Yes	11	15.1	1.02
Female	No	8	12.4	4.33
Female	Yes	10	11.5	3.96
Male	No	8	10.6	5.83
Male	Yes	7	11.5	6.12
Male	Yes	10	10.8	2.20
Male	Yes	11	12.5	2.93
Male	Yes	9	16.4	4.52
Female	Yes	2	14.1	4.50
Male	Yes	8	15.3	1.63
Female	No	6	18.0	3.09
Female	No	5	9.7	3.92
Male	Yes	11	10.5	3.10
Female	No	8	13.7	5.42
Male	Yes	8	14.9	2.03
Female	No	7	10.9	5.90
Male	No	10	14.5	3.25
Male	Yes	7	11.5	5.21
Female	No	9	11.3	3.31
Male	Yes	9	11.6	2.51
Male	No	10	15.6	3.88
Male	Yes	10	12.3	4.33
Male	Yes	11	12.2	4.49
Female	No	6	15.6	4.16
Male	Yes	11	11.0	4.99
Male	Yes	11	13.5	5.76
Female	No	7	11.0	3.54
Female	Yes	6	8.1	4.23
Male	Yes	8	17.6	3.66
Male	Yes	9	9.1	6.02
Male	Yes	12	13.5	3.56
Male	Yes	10	18.8	3.79
Female	No	8	12.8	4.59
Male	Yes	8	15.4	3.20
Male	Yes	9	12.6	0.98
Male	Yes	8	15.8	3.43
Male	Yes	8	14.2	5.68
Female	No	9	14.1	4.55
Female	No	6	14.7	3.16
Female	No	7	14.6	5.41
Female	No	4	10.1	4.31
Female	Yes	12	10.4	1.85
Female	No	7	11.2	3.87
Male	Yes	10	11.9	2.75
Male	Yes	10	8.2	6.77
Male	Yes	12	17.5	5.68
Male	Yes	11	8.4	5.26
Female	No	10	16.1	3.85
Male	No	7	13.4	6.07
Male	Yes	10	11.2	6.15
Male	Yes	10	17.5	4.75

A study investigated the impact of sleep deprivation on academic performance in university medical students. An individual's sleep habit was measured using a sleep quality index. A higher index number indicates poorer sleep quality. Academic performance was measured by the student's cumulative grade point average. In addition, the student's physical activity, as measured by the average time for exercise per week, and their behavioural risk factors such as alcohol use, smoking habit and coffee use were recoded.

The data contains the following variables:

GenderGender of the student (Male/Female)

Alcohol Whether the student drinks alcoholic beverages (Yes/No)

ExerciseAverage hours of exercise per week

SQISleep Quality Index (a higher index number indicates poorer sleep quality)

GPACumulative Grade Point Average

Question 1

The researchers claim that female students have better sleep quality than male students. The appropriate statistical test for their claim is a

Two-sample t-test

Chi-square test

Correlation test

Two-way ANOVA test

Question 2

Suppose F and M define the population mean sleep quality indices for females and males, respectively. The appropriate null and alternative hypotheses to test the claim in Question 1 are

H0:F>MvsH1:FM

H0:F=MvsH1:FM

H0:F=MvsH1:F>M

H0:F=MvsH1:F

Question 3

The test of the hypotheses in Question 2 indicates that there is

moderate evidence to suggest that female students have better sleep quality than male students (p = 0.024)

weak evidence to suggest that female students have better sleep quality than male students (p = 0.077)

no evidence to suggest that female students have better sleep quality than male students (p = 0.148)

no evidence to suggest that female students have better sleep quality than male students (p = 0.296)

Question 4

In general, if the study uses a smaller sample size, the probability of a Type II error will

decrease

stay the same

either increase or decrease

increase

Question 5

The association between academic performance and sleep quality is modelled using a simple linear regression. The appropriate population regression equation is

GPA=0+1SQI2+U

SQI=0+1GPA2+U

SQI=0+1GPA+U

GPA=0+1SQI+U

Question 6

The slope coefficient of the estimated linear regression equation in Question 5 is

-0.115

-0.084

-0.071

5.610

Question 7

The lower bound of a 95% confidence interval for the slope coefficient in Question 5 is

-11.353

-0.294

-0.250

-0.228

Question 8

Using the model in Question 5, the researcher examines whether there is a statistically significant negative linear relationship between academic performance and sleep quality. The researcher tests

H0:0=0vsH1:0>0

H0:1=0vsH1:10

H0:1=0vsH1:1<0

H0:1=0vsH1:1>0

Question 9

Using the model in Question 5, the p-value for the hypothesis test in Question 8 is

0.046

0.174

0.276

0.303

Question 10

The association between academic performance and sleep quality may be obscured by the students' engagement in physical activity and behavioural risk factors. Assuming there are no interactions, fit a multiple regression model for academic performance using sleep quality, exercise and alcohol usage as predictors. The estimated coefficient for the variable Exercise in this model is

-0.0192

-0.0142

-0.0070

0.0035

Question 11

In the fitted regression model in Question 10, the degrees of freedom used to test the statistical significance of the population parameter corresponding to the variable Exercise is

50

54

55

57

Question 12

Based on the model in Question 10, you can conclude that there is

weak evidence to suggest that academic performance is associated with exercise after taking into account the effect of sleep quality and alcohol usage (p = 0.094)

no evidence to suggest that academic performance is associated with exercise after taking into account the effect of sleep quality and alcohol usage (p = 0.703)

no evidence to suggest that academic performance is associated with exercise after taking into account the effect of sleep quality and alcohol usage (p = 0.822)

no evidence to suggest that academic performance is associated with exercise after taking into account the effect of sleep quality and alcohol usage (p = 0.971)

Question 13

Based on the fitted regression model in Question 10, the estimated cumulative grade point average of a student who drinks alcohol, has a sleep quality index of 15.5, and has an average 9 hours of physical exercise per week is

3.76

3.92

4.07

4.18

Question 14

A plot of residuals against fitted values for the model in Question 10 suggests that

the errors are right skewed

the errors are correlated

the errors are normally distributed

the errors have equal variance

Question 15

The regression sum of squares of the fitted model in Question 10 is

5.15

5.47

97.28

102.75

Do from question 10 to 15 only