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STA 2023 - Quiz 4 (Answer Key)
Spring 2003
Quiz proceedings:
 No cheating
 Show all relevant work to receive full credit – numbers in parentheses are point values for each problem
 Please turn off your cellular telephone
 Not permitted for use during the quiz: capri pants, sugar cane, lost teeth, Kangaroos™ shoes
 Good luck!
1. The business school at a university advertises that the GPA of the graduates of the M.B.A. program is
3.7. Test to see whether or not the school is incorrectly advertising an inflated GPA. Which choice best
reflects the test to be conducted? (4)
a. H0:  = 3.7, Ha:   3.7
b. H0:  = 3.7, Ha:  < 3.7
c. H0:  < 3.7, Ha:  > 3.7
d. H0: Hulk Hogan would crush Mr. T, Ha: Hulk Hogan would not crush Mr. T
2. TV Guide claims that the percentage of American adults, who want to see a Cheers reunion show, is
65%. Test to see whether or not this proportion is too high. In a random sample of 1,280 American
adults, the number who wanted to see a Cheers reunion show was 825. Which choice best reflects the
test to be conducted? (4)
a. H0:  = .65, Ha:  > .65
b. H0:  = .65, Ha:  < .65
c. H0:  < .65, Ha:   .65
d. H0: p = .65, Ha: p < .65
3. A survey wants to see if the proportion of males and the proportion of females who favor a certain
Democratic candidate are different, particularly if the proportion of males is less than that of the
females. Test to see if the true proportion of males is less than the true proportion of females. Which
choice best reflects the test to be conducted? (4)
a. H0: (pM – pF) = 0, Ha: (pM – pF)  0
b. H0: (pM – pF) = 0, Ha: (pM – pF) > 0
c. H0: (pM – pF) < 0, Ha: (pM – pF) > 0
d. H0: (pM – pF) = 0, Ha: (pM – pF) < 0
4. A consumer agency is doing a study on the average relief times of Advil and Tylenol. Determine
whether or not there is a significant in the average relief times. Which choice best reflects the test to be
conducted? (4)
a. H0: (A – T) = 0, Ha: (A – T)  0
b. H0: (A – T) < 0, Ha: (A – T) > 0
c. H0: (A – T) = 0, Ha: (A – T) < 0
d. H0: (A – T) = 0, Ha: (A – T) > 0
5. Investigators conducted a test concerning a nearby nuclear power plant in which the null and alternative
hypotheses are as follows: H0: The pollution is harmless, Ha: The pollution is harmful. Based on
research, investigators determined that the pollution was harmless and continued to let the nuclear power
plant operate unbridled. Several days later, a three-eyed fish (Blinky) was pulled from the local
reservoir, where its mutation was (correctly) blamed on the harmful pollution put forth by the power
plant (particularly Sector 7G). Which of the following best describes the decision and consequence
involved? (4)
a. A Type I Error was made
b. A Type II Error was made
c. A correct decision was made
d. Clancy framed Burns by placing the fish in the reservoir
6. Referring to the previous question, assume that the mutated fish was actually a new species of fish (not
due to pollution) and that no other evidence of harmful pollutants was found in years to come. Which of
the following best describes the decision and consequence involved? (4)
a. A Type I Error was made
b. A Type II Error was made
c. A correct decision was made
d. Vampires are make-believe just like elves, gremlins, and Eskimos
7. Identify the appropriate rejection region for testing H0:  = 36 versus Ha:  < 36 at the 10% significance
level. Assume that there were 38 subjects in the sample. (4)
a. Test Statistic > 1.28
b. Test Statistic < -1.28
c. Test Statistic < -1.645 or Test Statistic > 1.645
d. Test Statistic < -2.575
8. Identify the appropriate rejection region for testing H0:  = 36 versus Ha:  < 36 at the 5% significance
level. Assume that there were 18 subjects in the sample. (4)
a. Test Statistic < -1.645
b. Test Statistic < -1.740
c. Test Statistic < 1.740
d. Test Statistic < -1.734
9. Calculate the p-value when testing H0:  = 36 versus Ha:  < 36 at the 5% significance level, where we
observe a test statistic of –2.44 from a sample size of 38. (4)
a. .0073
b. .0146
c. .05
d. .4927
10. Calculate the p-value when testing H0:  = 36 versus Ha:  < 36 at the 5% significance level, where we
observe a test statistic of –1.94 from a sample of 18. (4)
a. .0262
b. .0524
c. .4738
d. Between .025 and .050
11. Suppose that a test yielded a p-value of .0166. What would our final decision be at the 5% significance
level? (4)
a. Reject H0
b. Reject Ha
c. Do not reject H0
d. Do not reject Ha
12. In general, under which situations should we reject the null hypothesis? (4)
a. When the test statistic falls in the rejection region or the p-value is greater than 
b. When the test statistic does not fall in the rejection region or the p-value is greater than 
c. When the test statistic does not fall in the rejection region or the p-value is less than 
d. When the test statistic falls in the rejection region or the p-value is less than 
13. Which is used to represent the null hypothesis? (4)
a. H0
b. Ha
c. 
d. 
14. In constructing a confidence interval for the difference between two independently sampled population
means, we found the following interval: 7 < 1 - 2 < 13. Is there evidence to suggest that the two
population means differ? (4)
a. Yes, since the interval does not include 0
b. Yes, since the interval includes 0
c. No, since the interval does not include 0
d. No, since the interval includes 0
15. Suppose that we were testing p = .45 against p < .45. Based on our sample we decide to reject the null
hypothesis. What is our conclusion? (4)
a. There is not enough evidence to suggest that p = .45
b. There is not enough evidence to suggest that p < .45
c. There is sufficient evidence to suggest that p = .45
d. There is sufficient evidence to suggest that p < .45
16. We wish to compare the average gas mileages of Lincoln Continentals and Cadillac El Dorados. By
driving 36 Lincolns we find the average miles per gallon to be 17.4 with a standard deviation of 6.2, and
by driving 36 Cadillacs we find the average miles per gallon to be 16.5 with a standard deviation of 5.6.
a. Construct a 95% confidence interval for the true mean difference. You do not have to interpret
the interval. (7)
x  x  z
1
2
/2
 
2
2
1
2
n
1
n
2
 17.4  16.5  1.96
6.2 2 5.6 2

 0.9  2.73  (-1.83, 3.63)
36
36
b. Is there evidence to suggest that there is a significant difference in gas mileage between the two
types of cars? Explain. (3) Since the interval constructed in part a includes 0, this suggests
that the two population means are equal, so there is not evidence to suggest a significant
difference in gas mileage.
17. The SCL-90-R is a 90-item symptom inventory checklist designed to reflect the psychological status of
an individual. Each symptom is scored on a scale of 0 to 4. The total of these scores yields an
individual’s Positive Symptom Total (PST). “Normal” individuals are known to have a mean PST of
about 40. The Journal of Head Trauma Rehabilitation reported that a sample of 33 patients diagnosed
with mild to moderate traumatic brain injury had a mean PST score of 48.43 and a standard deviation of
20.76. Is there sufficient evidence to claim that the true mean PST score of all patients with mild to
moderate traumatic brain injury exceeds the “normal” value of 40? Test using =.05. Be sure to show
all work, including, but not limited to, hypotheses, rejection region, critical value(s), test statistic,
p-value, and conclusion. If you make multiple attempts at a specific step, be sure that you
CLEARLY show which answer you want counted for credit, otherwise, you will receive only
partial credit. (15)
Hypotheses:
H0:  = 40
Ha:  > 40
Rejection Region:
Since Ha includes >, n  30 and  = .05, we should use z > 1.645 as our rejection region
Test Statistic:
x   0 48.43  40
z

 2.33

20.76
n
33
P-value:
Since Ha includes >, we should find the area (on the z-curve) to the right of 2.33:
p-value = P(z > 2.33) = .0099
Conclusion:
Since our test statistic falls in our rejection region, or, equivalently, our p-value is less than , we
should reject the null hypothesis. There is sufficient evidence to suggest that the true mean PST
score of all patients with mild to moderate traumatic brain injury exceeds the “normal” value of
40, at  = .05.
18. Researchers are conducting a survey to determine whether there is a difference of opinion between adult
males and females on the issue of capital punishment. In a survey of 196 males, 102 are in favor of
capital punishment, while 96 of 204 females are in favor of capital punishment. Is there sufficient
evidence to suggest that the proportion of males and females in favor of capital punishment are
significantly different, at the 5% significance level? Be sure to show all work, including, but not
limited to, hypotheses, rejection region, critical value(s), test statistic, p-value, and conclusion. If
you make multiple attempts at a specific step, be sure that you CLEARLY show which answer you
want counted for credit, otherwise, you will receive only partial credit. (14)
Hypotheses:
H0: (p1 – p2) = 0
Ha: (p1 – p2)  0
Sample Size Precondition:
x 102
x
96
pˆ 1  1 
 .52 , qˆ1  1  pˆ 1  1  .52  .48 , pˆ 2  2 
 .47 , qˆ 2  1  pˆ 2  1  .47  .53
n1 196
n2 204
pˆ 1  3
pˆ 1  qˆ1
.52  .48
 .52  3
 .52  .107  (.413, .627)  (0, 1)
n1
196
pˆ 2  qˆ 2
.47  .53
 .47  3
 .47  .105  (.365, .575)  (0, 1)
n2
204
Since both sample distributions lie well within the parameter space, the both sample sizes are
sufficiently large to use the standard normal approximation.
pˆ 2  3
Rejection Region:
Since Ha includes  and  = .05, we should use z < -1.96 and z > 1.96 as our rejection region
Test Statistic:
x  x2
102  96
pˆ  1

 .495 , qˆ  1  pˆ  1  .495  .505
n1  n2 196  204
( pˆ  pˆ 2 )  D0
(.52  .47)  0
z 1

 1.00
1 
1
 1
1 
.495  .505


pˆ qˆ   
 196 204 
 n1 n2 
P-value:
Since Ha includes , we should find the area (on the z-curve) to the right of 1.00, and double it:
p-value = 2P(z > 1.00) = 2(.1587) = .3174
Conclusion:
Since our test statistic does not fall in our rejection, or, equivalently, or our p-value is greater
than , we should not reject the null hypothesis. There is not enough evidence to suggest that
the true proportion of males and females who are in favor of capital punishment are significantly
different, at  = .05.
19. What is your biggest pet peeve? (1)
~ The End ~