Math 54 – Chapter 10 extra practice problems.
From Elementary Statistics, by Mario Triola
1. In a randomized controlled trial in Kenya, insecticide-treated bednets were tested as a
way to reduce malaria. Among 343 infants who used bednets, 15 developed malaria.
Among 294 infants who did not use bednets, 27 developed malaria. Use a 0.01 level of
significance to test the claim that the incidence (rate) of malaria is lower in infants who
used bednets.
2. Among 5000 items of randomly selected baggage handled by American Airlines, 22
were lost. Among 4000 items of randomly selected baggage handled by Delta airlines,
15 were lost. At the 0.05 level of significance, test the claim that the rates of lost
baggage are different for the two airlines.
3. In a USA Today article about the nasal spray flu vaccine for children, the data was
presented. For 1070 children two received the vaccine, 14 developed the flu. For 532
children who received a placebo, 95 developed the flu. At the 0.01 level of significance,
test the claim that the rate of the flu was lower for those receiving the vaccine. Does the
vaccine appear to be effective?
4. Many studies have been conducted to test the effects of marijuana on mental abilities.
In one such study, groups of light and heavy users of marijuana in college were tested for
memory recall, with the results given below. Use a 0.01 level of significance to test the
claim that the population of light users has a higher mean recall than that of heavy users.
Recall of light users: n  64, X  53.3, s  3.6
Recall of heavy users: n  65, X  51.3, s  4.5
5. Listed below are the fair market values (in thousands of dollars) of randomly selected
homes on Long Beach Island in New Jersey. Use a 0.05 level of significance to test a
realtor’s claim that oceanfront homes (directly on the beach) have a greater value than
oceanside homes, which are not directly on the beach.
Oceanfront:
Oceanside:
2199
700
3750
1355
1725
795
2398
1575
2799
759
6. One study used a CT scan to measure brain volume for two groups of patients. One
group had been diagnosed with obsessive compulsive disorder; they were compared to a
group of healthy patients. Use a 0.01 level of significance to test the claim that there is a
difference in the mean brain volume of the two groups.
Control Group: n=10, sample mean = 0.45, sample std. dev. = 0.08
Obsessive-Compulsive Patients: n = 10, sample mean = 0.34, sample std. dev = 0.08
7.As part of the National Health and Nutrition Examination Survey conducted by the
Department of Health and Human Services, the Dept. of Health and Human Services
obtained self-reported and measured heights of males aged 12 – 16. All of the
measurements were in inches. The results are given below. Note that the data is from 12
males in this age group and the reported and measured heights are from the same 12. So
for example, the first male reported a height of 68 inches and his measured height was
67.9. The second reported 71 inches and his measured height was 69.9 inches, etc.
Reported:
68
71
63
70
71
60
65
64
54
63
66
72
64.9
68.3
70.3
60.6
64.5
67.0
55.6
74.2
65.0
70.8
Measured:
67.9
69.9
At the 0.05 level of significance, test to determine if there is enough evidence to say that
there is a difference between reported and measured heights.
8. Listed below are the costs (in dollars) of flights from New York to San Francisco for 7
different airlines. The first list is the price for a flight scheduled 30 days in advance, the
second is for the same flight on the same airline scheduled one day in advance.
30 days:
244
260
264
264
278
318
280
1 day:
456
614
628
1088
943
567
536
a. At the 0.01 level of significance test to determine if the price for a 30-day advance
booking is less than the price of the 1-day advance.
b. Does this evidence show that it is better to book earlier?
Answers:
1. Population 1: used bednets
Population 2: did not use bednets
Ho: p1 = p2, Ha: p1 < p2, z = -2.44, p-value = 0.0074, Reject Ho. The sample data support the claim that
the incidence of malaria is lower in infants that use bednets.
(Possible Type I error)
2. Population 1: American Airlines
Population 2: Delta Airlines
Ho: p1 = p2, Ha: p1 ≠ p2, z = 0.48, p-value = 0.6320, Fail to Reject Ho. There is not sufficient
sample evidence to say that the rates of lost baggage are different for the two airlines. (possible type II
error)
3. Population 1: received vaccine
Population 2: did not receive vaccine
Ho: p1 = p2, Ha: p1 < p2, z = -12.39, p-value = 0, Reject Ho. There is sufficient sample evidence
to say that the rate of the flu was lower for those receiving the vaccine. It does appear that the vaccine is
effective. (possible type I error)
4. Population 1: light users
Population 2: heavy users
Ho: μ1 = μ2, Ha: μ1 > μ2, t = 2.79, p-value = 0.0031, Reject Ho. There is sufficient sample
evidence to say that the mean recall for light users was higher than the mean recall for heavy users.
5. Population 1: Oceanfront
Population 2: Oceanside
Ho: μ1 = μ2, Ha: μ1 > μ2, t = 3.99, p-value = 0.0.0035, Reject Ho, there is sufficient evidence to say that
oceanfront homes have a greater mean value.
6. Population 1: control group
Population 2: obsessive-compulsive patients
Ho: μ1 = μ2, Ha: μ1 ≠ μ2, t = 3.07, p-value = 0.0065, reject Ho, there is sufficient evidence to say that
there is a difference in mean brain volume.
7. (matched pair data)
Ho: μd = 0, Ha: μd ≠ 0, t = -0.98, p-value = 0.3461, fail to reject Ho, there is not sufficient evidence to
say that there is a difference in the reported and actual heights.
8. (matched pair data)
Ho: μd = 0, Ha: μd < 0, t = -4.71, p-value = 0.00164, reject Ho, there is sufficient evidence to say that the
mean price for a 30-day advance booking is less than the 1-day. It does seem like it is better to book
earlier.