CHS Statistics 8.1- 8.4 Review
Show all work on a separate sheet of paper.
1.) State the equations that are used for:
a.) Differences of two means, the sample is large and independent?
b.) Difference of means and dependent samples?
c.) Difference of proportions?
2.) Does stress affect the recall ability of police eyewitnesses? The numbers of details recalled a
week after an incident is summarized below. Use a 0.01 significance level to test the claim
that stress decreases the amount recalled.
Nonstress
Stress
n=40
n=40
mean = 53.3
mean = 45.3
S.D = 11.6
S.D = 13.2
3.) A study was made of 413 children who were hospitalized as a result of motor vehicle crashes.
Among 290 children who were not using seat belts, 50 were injured. Among 123 children
using seat belts, 16 were injured. Is there sufficient evidence to conclude that the rate of
severe injuries is lower for children wearing seat belts?
4.) Refer to the data set below that lists SAT scores before and after the sample of 10 students
took a preparatory course.
Student
before
after
A
B
C
D
E
F
G
H
I
J
700 840 830
860 840 690 830 1180 930 1070
720 840 820
900 870 700 800 1200 850 1080
a. Is there sufficient evidence to conclude that the preparatory course is effective in raising
scores? Use a 0.05 significance level.
b. Construct a 95% confidence interval estimate of the mean difference between the
before and after scores.
5.) When games were sampled from a season, it was found that the home team won 127 of 198
professional basketball games and the home team won 57 of 99 professional football games.
Construct a 95% confidence interval for the difference between the proportions of home wins.
6.) Data was collected on weights of men in two different age brackets. For 804 men ages 25-34,
the mean is 176 lb and a standard deviation of 35 lb. For 1657 men aged 65-74, the mean
and standard deviation are 164 lb and 27 lb respectively.
a. Test the claim that the older men come from a population with a mean that is less than
the mean for men in the 25-34 age bracket. Use a 0.01 significance level.
b. Construct a 99% confidence interval for the difference between the means of the men in
the two age brackets.
7.) A study was done on laboratory gloves. Among 240 vinyl gloves 63% leaked viruses. Among
240 latex gloves, 7% leaked viruses. At the 0.005 significance level, test the claim that vinyl
gloves have a larger virus leak rate than latex gloves.
8.) A study was conducted to investigate the effectiveness of hypnotism in reducing pain. Results
for randomly selected subjects are giving in the table. The values are before and after
hypnosis.
Subject
Before
After
A
B
C
D
E
F
G
6.6 6.5
9 10.3 11.3
8.1 6.3
6.8 2.4
7.4
8.5
8.1
6.1 3.4
a. Construct a 95% confidence interval for the mean of the before and after differences.
b. At the 0.05 significance level, test the claim that the sensory measurements are lower
after hypnotism.
c. Does hypnotism appear to be effective in reducing pain?