Download Chapter 7 Review

College Prep. Stats.
Chapter 7 Review
Name: _____________________________________
1. In a Pew Research Center poll of 745 randomly selected adults, 589 said that it is morally wrong to not report all income on tax
returns.
a) What is the best point estimate of the population proportion, p?
b) Find the critical value z* that corresponds to a 95% confidence level.
c) Calculate the margin of error, E, for the confidence interval used to estimate the population proportion, p.
d) Construct a confidence interval to estimate the population proportion, p.
e) Interpret the confidence interval you constructed in part (d).
f) Assume that you must conduct a new poll to determine the percentage of adults who believe that it is morally wrong to not report all
income on tax returns. How many randomly selected adults must you survey if you want 99% confidence that the margin of error is
two percentage points? ( p̂ and q̂ are unknown.)
g) Assume that you must conduct a survey to determine the mean income reported on tax returns, and you have access to actual tax
returns. How many randomly selected tax returns must you survey if you want to be 99% confident that the mean of the sample is
within $500 of the true population mean? Assume that reported incomes have a standard deviation of $28,785 (based on data from the
U.S. Census Bureau).
2. Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.04;
confidence level: 92%; from a prior study, p̂ is estimated by the decimal equivalent of 17%.
3. Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.01;
confidence level: 93%; pˆ and qˆ unknown.
4. A Gallup poll consisted of 1012 randomly selected adults who were asked whether “cloning of humans should or should not be
allowed.” Results showed that 901 adults surveyed indicated that cloning should not be allowed.
a) Find the best point estimate of the proportion of adults believing that cloning of humans should not be allowed.
b) Construct a 95% confidence interval estimate of the proportion of adults believing that cloning of humans should not be allowed.
5. The National Transportation Safety Administration conducted crash test experiments on five subcompact cars. The head injury data
(in hic) recorded from crash test dummies in the driver’s seat are as follows:
681, 428, 917, 898, 420
What is the best point estimate? Use proper notation with your answer.
6. Listed below are weights (in pounds) of glass discarded in one week by randomly selected households (based on data from the
Garbage Project at the University of Arizona).
3.52
8.87
3.99
3.61
2.33
3.21
0.25
4.94
a) What is the best point estimate of the mean weight of glass discarded by households in a week?
b) Construct a 95% confidence interval estimate of the mean weight of glass discarded by all households, if s = 2.457.
c) Construct a 95% confidence interval estimate of the mean weight of glass discarded by all households assuming that the population
is normally distributed with a standard deviation (σ) known to be 3.108 lb.
7. Lengths of fish: n = 102, x = 5.68 in., and σ = 1.1 in.
a) Find the critical value that corresponds to an 88% confidence level. State if your critical value is z* or t*.
b) Calculate the margin of error, E, for the confidence interval used to estimate the population mean, .
c) Construct an 88% confidence interval to estimate the population mean, µ.
8. Express the confidence interval 85.742 < µ < 115.321 in the form of x  E .
9. You have been hired by a consortium of local car dealers to conduct a survey about the purchases of new and used cars. If you want
to estimate the percentage of car owners in your state who purchased new cars (not used), how many adults must you survey if you
want 95% confidence that your sample percentage is in error by no more than four percentage points? ( p̂ and q̂ are unknown.)
10. Using problem number 9, if you want to estimate the mean amount of money spent by car owners on their last car purchase, how
many car owners must you survey if you want 95% confidence that your sample mean is in error by no more than $750? (Based on
results from a pilot study, assume that the standard deviation of amounts spent on car purchases is $14,227.)
11. A simple random sample of 37 weights of pennies made after 1983 has a mean of 2.4991 g and a standard deviation of 0.016 g
(based on Data Set 20 in Appendix B of your textbook). Construct a 99% confidence interval estimate of the mean weight of all such
pennies.
12. Assume we want to construct a confidence interval using the given confidence level. Do one of the following, as appropriate: (i)
Find the critical value zα/2 (z*), (ii) find the critical value tα/2 (t*), (iii) state that neither the normal nor the t distribution applies.
a) 93%; n = 34; σ is unknown; population appears to be normally distributed.
b) 90%; n = 102; σ is known; population appears to be normally distributed.
c) 98%; n = 18; σ is unknown; population appears to be very skewed.
d) 89%; n = 74; σ is unknown; population appears to be skewed.
e) 87%; n = 198; σ = 24.5; population appears to be skewed.
13. Lengths of fish: n = 102, x = 5.68 in., and s = 1.1 in.
a) Find the critical value that corresponds to an 88% confidence level. State if your critical value is z* or t*.
b) Calculate the margin of error, E, for the confidence interval used to estimate the population mean, .
c) Construct an 88% confidence interval to estimate the population mean, µ.
14. Assume that a sample is used to estimate a population proportion p. Find the margin of error, E, that corresponds to the given
statistics and confidence level. 93% confidence, sample size is 400, of which 42% are successes.
15. In a random sample of 547 elementary school students, 284 had pet dogs. Find the margin of error for the 90% confidence interval
used to estimate the population proportion.
16. The following confidence interval is obtained for a population proportion, p: (0.847, 0.912). Use these confidence interval limits
to find the point estimate, pˆ.
17. The following confidence interval is obtained for a population proportion, p: 0.748 < p < 0.922. Use these confidence interval
limits to find the point estimate, pˆ.
18. The following confidence interval is obtained for a population proportion, p: (0.847, 0.912). Use these confidence interval limits
to find the margin of error, E.
19. The following confidence interval is obtained for a population proportion, p: 0.748 < p < 0.922. Use these confidence interval
limits to find the margin of error, E.
20. Express the confidence interval 0.118 < p < 0.298 in the form pˆ  E.
21. Express the confidence interval (0.374, 0.498) in the form pˆ  E.
22. Find the margin of error for high school students’ annual earnings with 72% confidence; n = 64, x = $1,098, σ = $402.
23. Use the given information to find the minimum sample size required to estimate an unknown population mean µ. Margin of error:
7.24 in., confidence level: 84%, σ = 6.23 in.
24. How many women must be randomly selected to estimate the mean weight of women in one age group? We want 93% confidence
that the sample mean is within 10.68 lb. of the population mean, and the population standard deviation is known to be 6.32 lb.
25. Use the given confidence level and sample data to find the margin of error for the population mean µ. 96% confidence n = 8,
x = 0.987 and s = 0.17.
26. Use the given confidence level and sample data to find the confidence interval for the population mean µ. 96% confidence n = 8,
x = 0.987 and s = 0.17. Use the margin of error from number 25.
27. The following confidence interval is obtained for a population mean, µ: 85.742 < µ < 115.321. Use these confidence interval
limits to find the margin of error, E.
28. The following confidence interval is obtained for a population mean, µ: (174.847, 548.654). Use these confidence interval limits
to find the margin of error, E.
29. The following confidence interval is obtained for a population mean, µ: (174.847, 548.654). Use these confidence interval limits
to find the point estimate, x .