Quiz #15
Date:_________
Section: _______
Name: ________________________________
The following table lists the grade distribution for a sample of 160 students for Abe’s stat class,
Grade
Frequency
A
26
B
44
C
40
D
28
F
22
Total
Abe Claims that generally 25% of his students are getting grade of “A”, 15% “B”, 35% “C”, 10% “D” and 15 % “F”.
At 10% significance level, test Abe’s claim.
0
1. H0 hypothesis:
A. Stated claim is correct.
B. Stated claim is not correct
1. _________
2. Critical value: A. 11.07
B. 7.779
C. 9.488
D. 9.236
2. __________
3. Test statistics: A. 33.51
B. 29.53
C. 28.62
D. 35.31
3.___________
4. Conclusion:
4. __________
A. Accept that the stated claim is correct.
B. Reject that the stated claim is correct.
Let’s suppose you have reason to believe that students who work fewer than 20 hours a week have a higher GPA than students who
work 20 hours or more. We have two independent random samples: 120 ‘low intensity’ workers (group 1) and 120 ‘high intensity’
workers (group 2). The low intensity workers have an average GPA of 2.98 with a standard deviation of .44. The high intensity
workers have an average GPA of 2.01 with a standard deviation of .38. Do low intensity workers have significantly higher
GPAs than high intensity workers? Set  = .05
0
5. H0 hypothesis:
A.  1   2  0
B.  1   2  0 C.  1   2  0
D.  1   2  0
5. __________
6. Critical value:
A. 1.28
B. 1.28
C. 1.645
D. 1.645
6. __________
7. Test statistics:
A. 18.28
B. 17.21
C. 17.28
D. 19.45
7.___________
8. Comment:
A. Accept that the low intensity workers have significantly higher GPAs than high intensity workers.
B. Reject that the low intensity workers have significantly higher GPAs than high intensity workers.
8. __________
Participants in a random sample of 10 professional football players are placed on a yogurt-and-banana diet for one month. The
weights before and after one month on the diet are as follow:
Before:
After:
187
175
205
193
165
167
193
190
199
197
286
240
212
210
189
189
242
221
253
255
0
d=A-B
At 5% significance level, does the yogurt-and-banana diet help to reduce the weight of the football players.
9. H0 hypothesis:
A.
d
0
B.
d
0
C.
d
0
D.
d
0
9. __________
10. Critical value: A. 2.262
B. 1.833
C. 1.383
D. 2.262
10.__________
11. Test statistics: A. 2.00
B. 1.58
C. 2.00
D. 1.58
11.__________
12. Comment:
A. Accept that the yogurt-and-banana diet helps to reduce the weight of the football players.
B. Reject that the yogurt-and-banana diet helps to reduce the weight of the football players.
12. _________
1
Provide an appropriate response.
13) A company wants to determine if its employees have any preference among 5 different health
plans which it offers to them. A sample of 200 employees provided the data below. Calculate the
chi-square test statistic χ2 to test the claim that the probabilities show no preference. Use α = 0.01.
Plan
1 2 3 4 5
Employees 18 55 30 32 65
A) 45.91
B) 48.91
C) 37.45
13)
D) 55.63
14) A random sample of 160 car purchases are selected and categorized by age. The results are listed
below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39%
for the 26-45 group, 31% for the 45-65 group, and 12% for the group over 65. Calculate the
chi-square test statistic χ2 to test the claim that all ages have purchase rates proportional to their
14)
driving rates. Use α = 0.05.
Age
Under 26 26 - 45 46 - 65 Over 65
Purchases
66
39 25 30
A) 101.324
B) 75.101
C) 95.431
D) 85.123
15) Find the standardized test statistic to test the hypothesis that μ 1 = μ 2 . Two samples are randomly
selected from each population. The sample statistics are given below. Use α = 0.05.
n1 = 50
n2 = 60
x1 = 28
s 1 = 1.5
A) 8.1
x2 = 26
s 2 = 1.9
B) 3.8
C) 4.2
2
D) 6.2
15)