Ch.11 Review
CONFIDENCE INTERVALS
1. In 1996, the Gallup Organization surveyed 535 adults aged 18 years old or older and asked, “Do you think there is
some form of life on other planets in the universe?”. Of the 535 individuals surveyed, 326 responded “yes”. When
the same question was asked in 1999, 335 out of 535 individuals responded “yes”. Construct a 99% confidence
interval estimate of the difference between the proportion of people who said yes in 1996 and the proportion of
people who said yes in 1999. Is there a significant difference between the two proportions?
2. An automotive researcher wants to estimate the difference in the distance required to come to a complete stop
while traveling 40 mph on wet versus dry pavement. The researcher used 8 different cars with the same driver and
tires. The braking distance, in feet, on both wet and dry pavement is shown below. Construct a 95% confidence
interval estimate of the mean difference in braking distances between wet and dry pavement. Is there a significant
difference between the mean braking times?
Car #
Wet
Dry
1
106.9
71.8
2
100.9
68.8
3
108.8
74.1
4
111.8
73.4
5
105.0
75.9
6
105.6
75.2
7
110.6
75.7
8
107.9
81.0
3. In packaging drinks, the aluminum bottle is reported to cool faster and stay cold longer than typical glass bottles.
A small brewery tests this and obtains the following information regarding the time (in minutes) required to chill a
bottle of beer from room temperature (75ºF) to serving temperature (45ºF). Construct a 90% confidence interval
estimate for the difference in the mean cooling times for clear glass versus aluminum bottles. Is there a significant
difference between the mean cooling times?
Clear Glass
Aluminum
n = 42
n = 35
x = 133.8
x = 92.4
s = 9.9
s = 7.3
HYPOTHESIS TESTING
1. Hemoglobin helps the red blood cells transport oxygen and remove carbon dioxide. Researchers at NASA
wanted to determine the effects of space flight on a rat’s hemoglobin level. The following data represent the
hemoglobin levels before lift-off and immediately upon the return for 12 randomly selected rats sent to space. Test
the claim that the hemoglobin levels before lift-off are less than the hemoglobin levels upon return. Use α = 0.05.
Rat
1
Liftoff 15.2
Return 15.8
2
16.1
16.5
3
15.3
16.7
4
16.4
15.7
5
15.7
16.9
6
14.7
13.1
7
14.3
16.4
8
14.5
16.5
9
15.2
16.0
10
16.1
16.8
11
15.1
17.6
12
15.8
16.9
2. A researcher wanted to determine if business travelers walk at a different pace than leisure travelers. The
researcher measured the walking speed of business and leisure travelers in two major airports. For 20 business
travelers, the average speed was 272 ft/min with a standard deviation of 43 ft/min. For 25 leisure travelers, the
average speed was 261 ft/min with a standard deviation of 47 ft/min. Assume both samples come from populations
that are normally distributed. Test the claim that the business travelers walk at a different average speed than the
leisure travelers. Use α = 0.01.
3. In 1955, Dr. Jonas Salk released the results of clinical trials for his vaccine to prevent polio. In these clinical trials,
400,000 children were randomly divided into two groups. The subjects in one group were given the vaccine, while
the subjects in the other group were given a placebo. Of the 200,000 children given the vaccine, 33 developed polio.
Of the 200,000 children given the placebo, 115 developed polio. Test the claim that the proportion of subjects who
contracted polio is smaller in the vaccine group than the placebo group. Use α = 0.01.
Ch.11 Review
ANSWERS:
1. 2-Proportion Z-Interval
(–0.0933, 0.0597) There is NO significant difference between the proportions. (0 is in the interval)
2. T-Interval (matched pairs) Put “Wet” data in L1. Put “Dry” data in L2. Make L3 = L1 – L2.
(29.551, 35.849) (feet) There is a significant difference in the braking distances. (0 not in the interval)
3. 2-SampleT-Interval (Not pooled)
(38.129, 44.671) (min) There is a significant difference in the mean cooling times. (0 not in the interval)
1. T-test (matched pairs)
Put “Liftoff” in L1. Put “Return” in L2.
Make L3 = L1 – L2.
2. 2-SampleT-Test
(Not pooled)
Group 1 is “business”
Group 2 is “leisure”
I. Ho: μd = 0
H1: μd < 0 (claim)
II. α = 0.05
III. Test Statistic = –2.61
IV. P-value = 0.0120
V. Reject Ho
Conclusion: There is sufficient evidence to conclude
I. Ho: μ1 = μ2
H1: μ1 ≠ μ2 (claim)
II. α = 0.01
III. Test Statistic = 0.82
IV. P-value = 0.4179
V. Do not Reject Ho
Conclusion: There is not sufficient evidence to
that the hemoglobin levels before lift-off are less than the
hemoglobin levels upon return.
conclude that the business travelers walk at a different
average speed than the leisure travelers.
3. 2-Proportion-ZTest
Group 1 is “vaccine”
Group 2 is “placebo”
I. Ho: p1 = p2
H1: p1 < p2 (claim)
II. α = 0.01
III. Test Statistic = –6.74
IV. P-value = 0
V. Reject Ho
Conclusion: There is sufficient evidence to conclude
that the proportion of subjects who contracted polio is
smaller in the vaccine group than the placebo group.