AP Statistics
The First Eight Procedures
1. In a study of air-bag effectiveness, it was found that in 821 crashes of midsize cars equipped with air
bags, 46 of the crashes resulted in hospitalization of the drivers. Give a 95% confidence interval for
the percent of crashes resulting in hospitalization.
2. Consumer Reports gave the following information about annual premiums (in dollars) for 18
renewable life insurance policies with similar benefits:
300
345
328
426
660
388
410
563
303
395
278
455
577
470
455
373
365
360
Find a 98% confidence interval for the population of all annual premiums for such life insurance
policies.
3. “Obesity raises heart-attack risk” according to a study published in the March 1990 issue of the New
England Journal of Medicine. “Those about 15 to 25 percent above desirable weight had twice the
heart disease rate.” Suppose the data listed below are the percentages above desired weight for a
sample of patients involved in a similar study.
18.3
22.5
21.9
19.7
16.5
22.1
13.0
19.2
22.1
17.5
27.7
12.7
17.9
22.0
22.2
17.2
18.1
21.1
22.4
16.2
17.3
19.9
13.3
21.5
22.1
19.8
16.3
Is there evidence to conclude that the mean percentage above desired weight is 18%? Use a 2%
significance level.
4. Gregor Mendel, an Austrian monk, proposal the genetic theory of inheritance in 1866. He supported
his theory with the results of 8 years of experiments breeding peas and examining the inheritance of
seven different characteristics. One characteristic studied was plant height. Mendel crossed
purebred tall plants with purebred short plants. He proposed that when he bred these hybrids, onequarter of their progeny would be pure short. Mendel reported that out of 1,064 randomly selected
plants, 277 were short. Does he have the evidence to support his theory?
5. Suppose you wish to compare a new method of teaching reading to “slow learners” to the current
standard method. You decide to base this comparison on the results of a reading test given at the end
of a learning period of 6 months. Of a random sample of 20 slow learners, 8 are taught by the new
method and 12 are taught by the standard method. All 20 children are taught by qualified instructors
under similar conditions for a 6-month period. The results of the reading test at the end of this
period are given below.
New Method
Standard 79
80
62
80
70
Reading Scores for Slow Learners
79
81
76
66
79
68
73
76
86
73
76
72
68
75
66
Use a 90% confidence interval, and interpret the interval for the true mean difference between the
test scores for the new method and the standard method.
6. Some college professors make bound lecture notes available to their classes in an effort to improve
teaching effectiveness. Because students pay the additional cost, educators want to know whether
the students consider the lecture notes to be a good educational value. Marketing Educational
Review (Fall 1994) published a study of business students’ opinions of lecture notes. Two groups of
students were surveyed-86 students enrolled in a promotional strategy class that required the
purchase of lecture notes, and 35 students enrolled in a sales/retailing elective that did not offer
lecture notes. In both courses, the instructor used lectures as the main method of delivery. At the
end of the semester, the students were asked to respond to the statement: “Having a copy of the
lecture notes was [would be] helpful in understanding the material.” Responses were measured on a
9-point semantic difference scale, where 1 = “strongly disagree” and 9 = “strongly agree.” A
summary of the results is shown in the table below.
Classes Buying Lecture
Classes Not Buying
Notes
Lecture Notes
mean score = 8.48
mean score = 7.80
standard deviation = 0.94
standard deviation = 2.99
Test to see if the scores of classes buying lecture notes is higher than the scores of classes not buying
lecture notes.
7. In the late 70’s there were intensive antismoking campaigns sponsored by both federal and private
agencies. Suppose that the American Cancer Society randomly sampled 1,500 adults in 1979 and
then sampled 2,000 adults in 1981 to determine whether there was evidence that the percentage of
smokers had decreased.
1979 1981
Sample Size
1500 2000
Number Who Smoke 576 652
Give a 90% confidence interval for the difference between the proportion of smokers in 1979 and the
proportion of smokers in 1981. Interpret the interval.
8. A random sample of 288 voters registered in the state of California showed that 141 voted in the last
general election. A random sample of 216 registered voters in the state of Colorado showed that 125
voted in the most recent general election. (Taken from Life in the Fifty States, G. S. Thomas) Do
these data indicate that the population proportion of voter turnout in Colorado is higher than that in
California?
9. A random sample of students from a high school were chosen to determine if their sitting pulse rate
was lower than their standing pulse rate. Each student’s pulse rate was measured in both positions.
Sitting
62 74 82 88 82 66
Standing
68 78 80 92 58 96
Can we conclude the sitting pulse rate is lower?
64
72
84
100
72
82
82
76
80
92
72
74
64
60
62
58