AP Statistics – Chapters 23-25 Review Worksheet
Name_____________________________
1. A national poll reported that average wages had reached a record high of $21,300. In order to
determine how the city compared to the national mean, the chamber of commerce gathered data
from the 25 largest employers and obtained an average of $22,750 with a standard deviation of
$2750. Can the chamber support the claim that the city is significantly different from the national
average at the 0.01 level?
2. A sampling of 50 random women and 40 random men produced a mean age at death of 75.5 years
for women and 67.9 years for men with standard deviations of 16.2 years (women) and 18.3 years
(men). At the 0.05 level of significance, do women live longer than men?
3. There is discussion in the media of grade inflation; that is, average grades rising over time. To
determine if grade averages are really higher now than in the past, Professor Smith gathered
records from 90 randomly selected students to compare to the mean of 2.54 that existed 10 years
ago. The 90 students produced a grade average of 2.69 with a standard deviation of 0.96. At the
0.05 level of significance, are grade averages higher than in the past?
4. A researcher wishes to determine whether the salaries of professional nurses employed by private
hospitals are higher than those of nurses employed by government-owned hospitals. She selects a
random sample of nurses from each type of hospital and calculates the means and standard
deviations of their salaries. Private hospital nurses had a mean salary of $26,800 with a standard
deviation of $600 (sample of 10 nurses), while the government-owned hospital nurses had a mean
salary of $25,400 with a standard deviation of $450 (sample of 8). At the 0.01 level, can she
conclude that the private hospitals pay more than the government hospitals? It is known that
salaries vary normally.
5.
A physical education director claims that by taking 800 international units (IU) of vitamin E, a
weight lifter can increase his strength. Eight athletes are randomly selected and given a test of
strength, using the standard bench press. After two weeks of regular training, supplemented with
vitamin E, they are tested again. Test the effectiveness of the vitamin E regimen at the 0.05 level
of significance. Each value in the data that follow represents the maximum number of pounds the
athlete can bench-press. Assume the data is normally distributed.
Athlete
1
2
3
4
5
6
7
8
Before
210
230
182
205
262
253
219
216
After
219
236
179
204
270
250
222
216
6. Find a 99% confidence interval of the difference between IQ scores for students in schools in two
different ethnic neighborhoods. A random sample of 75 was taken from school A with a mean of
105 and standard deviation of 10.2, while a random sample of 60 was taken from school B with a
mean score of 108 and a standard deviation of 12.4.
7. Find a 90% confidence interval that represents the effectiveness of the vitamin E regimen described
in # 5.
8.
A local coach has a theory, based on his experience, that participants in sports which stress
individual achievement do better academically than those who participate in team sports. He
believes that the skills required for individual success, such as motivation and self-discipline, carry
over to academic areas. To test his theory, he collected the following data on cumulative gradepoint averages of female athletes: team sport participants sample of 7 with mean 2.56 and standard
deviation 0.871, individual sport participants sample of 8 with mean 3.04 and standard deviation
0.621. Is his assumption justified at the 0.05 level of significance? Samples were randomly
selected and grade point averages vary normally.
9. To examine seasonal average in volume of stock trades, in millions of shares, the following data
were gathered. Is the average volume of trades greater in the fall, at the 0.05 level of significance?
Fall
Spring
SRS size
26
31
mean
45
38.2
standard deviation
5.2
3.9
10. A maker of frozen meals claims that the average caloric content of its meals is 800. A researcher
tested an SRS of 12 meals and found that the average number of calories was 873 with a standard
deviation of 25. Caloric content varies normally. Is there enough evidence to reject the claim at
 = 0.02?
11. A sports shoe manufacturer claims that joggers who wear its brand of shoe will jog faster than
those who don’t use its product. An SRS of eight joggers is taken and the joggers agree to test the
claim on a 1-mile track. The rates (in minutes) of the joggers while wearing the manufacturer’s
shoe and while wearing any other brand of shoe are shown. Test the claim at  = 0.025.
Runner
Manufacturer’s
Brand
Other Brand
1
8.2
2
6.3
3
9.2
4
8.6
5
6.8
6
8.7
7
8.0
8
6.9
7.1
6.8
9.8
8.0
5.8
8.0
7.4
8.0
12. A researcher estimates that high school girls miss more days of school than high school boys. A
sample of 16 girls showed that they missed an average of 3.9 days of school per school year; a
sample of 22 boys showed that they missed an average of 3.6 days of school per year. The
standard deviations are 0.6 and 0.8, respectively. At the 1% level of significance, test the claim.
13. The average hemoglobin reading for an SRS of 20 teachers was 16 grams per 100 milliliters, with a
sample standard deviation of 2 grams. Find the 99% confidence interval of the true mean.
14. A study of teenagers found that a random sample of 50 boys talked on the phone an average of 21
minutes per conversation with a standard deviation of 2.1. A random sample of 50 girls talked on
the phone an average of 18 minutes with a standard deviation of 3.2. Find the 95% confidence
level of the true differences in means.