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Homework 2
Chapter 9
34. A population proportion is 0.4. A simple random sample of size 200 will be taken
and the sample proportion p will be used to estimate the population proportion.
a. What is the probability that the sample proportion will be within  0.03 of the
population proportion?
b. What is the probability that the sample proportion will be within  0.05 of the
population proportion?
36. The population proportion is 0.3. What is the probability that the sample
proportion will be within  0.04 of the population proportion for each of the
following sample sizes?
a. n  100 b. n  200 c. n  500 d. n  1000 e. What is the advantage of a
larger sample size?
39. Louis Harris & Associates conducted a survey of 403 senior executives to learn
about how they view the U.S. economy for the coming 12 months (Business Week,
June 16, 1997). Assume that for the entire population of executives, 80% are
optimistic about the U.S. economy. Let p be the sample proportion of polled
executives who are optimistic about the U.S. economy.
a. Show the sampling distribution of p if the population proportion is p  0.8 .
b. What is the probability that the Harris poll sample proportion will be within
 0.02 of the population proportion?
c. What is the probability that the Harris poll sample proportion will be within  0.03
of the population proportion?
43. The Food Marketing Institute shows that 17% of households spend more than
$100 per week on groceries (U.S.A Today, June 21, 1994). Assume the population
proportion is p  0.17 and a simple random sample of 800 households will be
selected from the population.
a. Show the sampling distribution of p , the sample proportion of households
spending more than $100 per week on groceries.
b. What is the probability that the sample proportion will be within  0.02 of the
population proportion?
c. Answer part (b) for a sample of 1600 households.
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Chapter 10
3. A sample of 60 items resulted in a sample mean of 80 and a sample standard
deviation of 15.
a. Compute the 95% confidence interval for the population mean.
b. Assume that the sample mean and sample standard deviation were obtained from a
sample of 120 items. Provide a 95% confidence interval for the population mean.
c. What is the effect of a large sample size on the interval estimate of a population
mean?
5. In an effort to estimate the mean amount spent per customer for dinner at a major
Atlanta restaurant, data were collected for a sample of 49 customers over a three-week
period.
a. Assume a population deviation of $2.50. What is the standard error of the mean?
b. At a 95% confidence level, what is the margin of error?
c. If the sample mean is $22.6, what is the 95% confidence interval for the population
mean?
11. J.D. Power & Associates’ annual quality survey for automobiles found that the
industry average number of defects per new car is 1.07 (The Wall Street Journal,
January 27, 1994). Suppose a sample of 30 new automobiles taken by a particular
manufacturer provides the following data on number of defects per car.
0
1
1
2
1
0
2
3
2
1
0
4
3
1
1
0
2
0
0
2
3
0
2
0
2
0
3
1
0
2
a. Using these data, what is the sample mean number of defects per car?
b. What is the sample standard deviation?
c. Provide a 95% confidence interval estimate of the mean number of defects per
car for the population of cars produced by this manufacturer.
d. After reviewing the confidence interval estimate in part (c), a statistical analyst
suggested that the manufacturer test a large number of new cars before drawing
a conclusion about how the quality of its cars compares to the J. D. Powers &
Associates industry average of 1.07 defects per car. Do you support this idea?
Why or why not?
13. For a t distribution with 12 degrees of freedom, find the area, or probability,
that is in each region.
a. To the left of 1.782.
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b. To the right of -1.356.
c. To the right of 2.681.
d. To the left of -1.782.
e. Between -2.179 and +2.179.
f. Between -1.356 and +1.782.
15. The following data have been collected for a sample from a normal population:
10
8
12
15
13
11
6
5
a. What is the point estimate of the population mean?
b. What is the point estimate of the population standard deviation?
c. What is the 95% confidence interval for the population mean?
17. In the testing of a new production method, 18 employees were selected randomly
and asked to try the new method. The sample mean production rate for the 18
employees was 80 parts per hour and the sample standard deviation was 10 parts per
hour. Provide 90% and 95% confidence intervals for the population mean production
rate for the new method, assuming the population has a normal probability
distribution.
21. The U.S. Department of Transportation reported the number of miles that
residents of metropolitan areas travel per day in a car (1994 Information Please
Environmental Almanac). Suppose a simple random sample of 15 residents of
Cleveland provided the following data on car miles per day.
20
20
28
16
11
17
23
22
18
10
22
29
19
32
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a. Compute a 95% confidence interval estimate of the population mean number of
miles residents of Cleveland travel per day in a car.
b. What assumption about the population was necessary to obtain an answer to part
(a).
c. Suppose it is desirable to estimate the population mean number of miles with a
margin of error of  2 miles at 95% confidence. Do the data provide this desired
level of precision? What action, if any, would you recommend be taken?
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