Download Ch. 7 – Estimates and Sample Sizes 1. The mean and standard

Ch. 7 – Estimates and Sample Sizes
1. The mean and standard deviation, respectively, of students working after school are
17.6h and 9.3h. The given statistics are based on a sample size of 50 drawn from a
normally distributed population.
a. Find the best point estimate of the population mean.
b. Find a 95% confidence interval estimate of the population mean.
Use:
•
AND
̅
̅
√
c. When do you use the Student
2. Find the value of
(A)
(B)
(C)
(D)
distribution, instead of a
distribution?
that corresponds to a confidence level of 97.80%.
2.29
0.011
2.01
2.29
3. How many students must be surveyed if a psychologist wants 96% confidence that a
sample proportion is in error by no more than .06?
Use:
OR
.
4. Use the given degree of confidence and sample data to find a confidence interval for
the population standard deviation . Assume that the population has a normal
distribution.
College students' annual earnings: 98% confidence; 9, ̅ $3705,
$841
(A)
(B)
(C)
(D)
$568
$511
$662
$531
$1611
$1646
$1097
$1854
5. The Newton Car Park is a dealership considering newspaper advertising targeted at
women buyers. A marketing study found that 312 of 650 randomly selected buyers of
compact cars were women (based on the Ford Motor Company). Construct a 95%
interval estimate for the true percentage of all compact car buyers who are women.
̂
̂
̂
6. 364 randomly selected light bulbs were tested in a laboratory, 124 lasted more than
500 hours. Find a point estimate of the proportion of all light bulbs that last more
than 500 hours.
(A)
(B)
(C)
(D)
0.338
0.341
0.254
0.659
7. A sociologist develops a test to measure attitudes about public transportation, and 25
randomly selected subjects are given the test. Their mean score is 76.2 and their
population standard deviation is 21.4. Construct the 95% confidence interval for the
mean score of all such subjects.
Use
•
and ̅
̅
√
8. Assume that a sample is used to estimate a population proportion . Find the
margin of error that corresponds to the given statistics and confidence level.
95% confidence; the sample size is 6100, of which 40% are successes
(A) 0.00923
(B) 0.1041
(C) 0.1062
(D) 0.1023
9. A study was conducted to estimate hospital costs for accident victims who
wore seat belts. Twenty randomly selected cases have a distribution that appears to
be bell-shaped with a mean of $9004 and a standard deviation of $5629. Construct
the 99% confidence interval for the mean of all such costs. If you are a manager for
an insurance company that provides lower rates for drivers who wear seat belts, and
you want a conservative estimate for a worst-case scenario, what amount should you
use as the possible hospital cost for an accident victim who wears seat belts?
•
̅
̅
√
10. Find the critical value
95 percent.
(A)
(B)
(C)
(D)
corresponding to a sample size of 4 and a confidence level of
0.216
0.352
9.348
7.815
11. Use the given degree of confidence and sample data to construct a confidence interval
for the population mean . Assume that the population has a normal distribution.
12, ̅ 21.9,
4.0 , 99% confidence
(A)
(B)
(C)
(D)
18.31
18.24
18.33
18.76
25.49
25.56
25.47
25.04
12. Of 366 randomly selected medical students, 27 said that they planned to work in a
rural community. Find a 95% confidence interval for the true proportion of all medical
students who plan to work in a rural community.
(A)
(B)
(C)
(D)
0.0513
0.0386
0.0470
0.0419
0.0962
0.109
0.101
0.106