Statistics Worksheet

Question 1 (25 points)An online survey claimed that household income of athletes vary by sport. In order to
verify this claim, five sports enthusiasts are sampled who participate in 6 different sports
and obtains the income (in $1,000s)
Snorkeling Sailing
Windsurfing
Bowling
Triathalon
Off
road
Triathalon
90.9
87.6
75.9
79.3
64.5
47.7
86
95
75.6
75.8
67.2
59.6
93.6
94.6
83.1
79.6
62.8
68
98.8
87.2
74.4
78.5
59.2
60.9
98.4
82.5
80.5
73.2
66.5
50.9
•
•
•
Construct an ANOVA table. Assume incomes are normally distributed.
Specify the competing hypotheses to test whether there are some differences in
the incomes depending on the sport. At the 5% significance level, do average
incomes differ depending on the recreational sport?
If there is a difference above, choose four pairs of sports to compare and let us
know if there is a difference among those sports.
Question 2 (25 points)
2. What goes into a checklist for Regression diagnostics? In your own
words, from the beginning step to the final model, what are the
important things to be looking for?
Question 3 (25 points)
3. 50 observations were used to estimate
Wage = βo + β1 (Education) + β2 (Experience) + β3(Age) + ε
Wage is the hourly wage rate and Education/Experience/Age are the
years of higher education, years of experience and age of the worker
respectively.
These are the Excel results:
Coefficients
Standard
Error
t-Stat
p-value
Intercept
7.87
4.09
1.93
0.0603
Education
1.44
0.34
4.24
0.0001
Experience
0.45
0.14
3.16
0.0028
Age
-0.01
0.08
-0.14
0.8920
• What is the estimate for β1 and β2? Interpret these values.
• What is the sample regression equation?
• Predict the hourly wage for a 30 year old worker with 4 years of
higher education and 3 years of experience.
Question 4 (25 points)
A manager of an industrial plant asserts that workers on average do not complete a job
using Method A in the same amount of time as they would using Method B. Seven
workers are randomly selected. Each worker’s completion time (in minutes) is recorded
by the use of Method A and Method B.
Worker
Method A
Method B
1
2
3
15
21
16
16
25
18
4
5
6
18
19
22
22
23
20
7
20
20
a. Specify the null and alternate hypotheses to test the manager’s assertion.
b. At the 10% significance level, specify the critical value(s) and decision rule.
c. Assuming the completion time difference is normally distributed, calculate the
value of the test statistic.
d. Is the manager’s assertion supported by the data?