Chapter 9: Sampling Distributions and Confidence Intervals for Proportions
– Quiz A
Name ________________________________________
9.2.6 Find and interpret margins of error.
1. In a metal fabrication process, metal rods are produced to a specified target length of
15 feet. Suppose that the lengths are normally distributed. A quality control specialist
collects a random sample of 16 rods and finds the sample mean length to be 14.8 feet and
a standard deviation of 0.65 feet.
a. Describe the sampling distribution for the sample mean.
b. What is the standard error?
c. For 95% confidence, what is the margin of error?
d. Based on the sample results, create the 95% confidence interval and interpret.
9.2.7 Find and interpret confidence intervals.
2. A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on
data collected from its automatic filling process, the amount of cheese inserted into the
ravioli is normally distributed. To make sure that the automatic filling process is on
target, quality control inspectors take a sample of 25 ravioli and measure the weight of
cheese filling. They find a sample mean weight of 15 grams with a standard deviation of
1.5 grams.
a. Describe the sampling distribution for the sample mean.
b. What is the standard error?
c. What is the margin of error for 99% confidence?
d. What is the margin of error for 90% confidence?
e. Based on the sample results, find the 99% confidence interval and interpret.
f. Based on the sample results, find the 90% confidence interval and interpret.
g. For a more accurate determination of the mean weight, the quality control inspectors
wish to estimate it within .25 grams with 99% confidence. How many ravioli should they
sample?
9-2 Chapter 9 Sampling Distributions and Confidence Intervals for Proportions
9.2.6 Find and interpret confidence intervals.
3. Insurance companies track life expectancy information to assist in determining the
cost of life insurance policies. Last year the average life expectancy of all policyholders
was 77 years. ABI Insurance wants to determine if their clients now have a longer life
expectancy, on average, so they randomly sample some of their recently paid policies.
The ages of the clients in the sample are shown below.
86 75 83 84 81 77 78 79 79 81
76 85 70 76 79 81 73 74 72 83
a. Based on the sample results, find the 90% confidence interval and interpret.
b. For more accurate cost determination, ABI Insurance wants to estimate the average life
expectancy to within one year with 95% confidence. How many randomly selected
recently paid policies would they need to sample?
c. Suppose ABI samples 100 recently paid policies. This sample yields a mean of 77.7
years and a standard deviation of 3.6 years. Find a 90% confidence interval and interpret.
9.1.2 Find the mean and standard deviation of proportions.
4. Suppose that the store chain of Electronics Plus sells extended warranties to 20% of
customers who purchase electronic devices. A local Seattle store samples 300 customers
from their data base.
a. What proportion of customers would they expect to have purchased extended
warranties?
b. What is the standard deviation of the sample proportion?
c. What shape would you expect the sampling distribution of the proportion to have?
d. Would you be surprised to find out that in a sample of 300, 40 of the customers
purchased extended warranties? Explain. What might account for this high percentage?
Quiz A 9-3
Chapter 9: Sampling Distributions and Confidence Intervals for Proportions
– Quiz A – Key
9-4 Chapter 9 Sampling Distributions and Confidence Intervals for Proportions
Quiz A 9-5
9-6 Chapter 9 Sampling Distributions and Confidence Intervals for Proportions
Quiz B 9-7
Chapter 9: Sampling Distributions and Confidence Intervals for Proportions
– Quiz B
Name ________________________________________
9.2.6 Find and interpret confidence intervals.
1. A small business ships specialty homemade candies to anywhere in the world. Past
records indicate that the weight of orders is normally distributed. Suppose a random
sample of 16 orders is selected and each is weighed. The sample mean was found to be
110 grams with a standard deviation of 14 grams.
a. Describe the sampling distribution for the sample mean.
b. What is the standard error?
c. For 90% confidence, what is the margin of error?
d. Based on the sample results, create the 90% confidence interval and interpret.
9.2.6 Find and interpret confidence intervals.
2. Grandma Gertrude’s Chocolates, a family owned business, has an opportunity to
supply its product for distribution through a large coffee house chain. However, the
coffee house chain has certain specifications regarding cacao content as it wishes to
advertise the health benefits (antioxidants) of the chocolate products it sells. In order to
determine the mean % cacao in its dark chocolate products, quality inspectors sample 36
pieces. They find a sample mean of 55% with a standard deviation of 4%.
a. Describe the sampling distribution for the sample mean.
b. What is the standard error?
c. What is the margin of error for 90% confidence?
d. What is the margin of error for 95% confidence?
e. Based on the sample results, find the 90% confidence interval and interpret.
f. Based on the sample results, find the 95% confidence interval and interpret.
g. For a more accurate determination of the mean weight, the quality control inspectors
wish to estimate it within 1% with 95% confidence. How many pieces of dark chocolate
should they sample?
9-8 Chapter 9 Confidence Intervals and Hypothesis Tests for Means
9.2.6 Find and interpret confidence intervals.
3. A large software development firm recently relocated its facilities. Top management
is interested in fostering good relations with their new local community and has
encouraged their professional employees to engage in local service activities. They wish
to determine the average number of hours the firm’s professionals volunteer per month.
A random sample of 24 professionals reported the following number of hours:
12 13 14 14 15 15 15 16 16 16 16 16
17 17 17 18 18 18 18 19 19 19 20 21
a. Based on the sample results, find the 95% confidence interval and interpret.
b. For a more accurate determination, top management wants to estimate the average
number of hours volunteered per month by their professional staff to within one hour with
99% confidence. How many randomly selected professional employees would they need
to sample?
c. Suppose 40 professional employees are randomly selected. This sample yields a mean
of 15.2 hours and a standard deviation of 1.8 hours. Find a 95% confidence interval and
interpret.
9.4.8 Find sample sizes.
4. A clothing store is about to send out an electronic mailing to test the market for a
specific credit card for their store. From that sample, the want to estimate the true
proportion of people who will sign up for the card nationwide. To be within a tenth of a
percentage point, or 0.001 of the true rate with 90% confidence, how big does the mailing
have to be? Similar mailings in the past lead them to expect about 0.5% of the people
receiving the offer will accept it.
9.2.6 Find and interpret confidence intervals.
5. EU (European Union) countries report that 46% of their labor force is female. The
United Nations wants to determine if the percentage of females in the U.S. labor force is
the same. Representatives from the United States Department of Labor plan to check a
random sample of over 10,000 employment records on file to estimate the percentage of
females in the U.S. labor force.
a. The Department of Labor wants to estimate the percentage of females in the U.S. labor
force to within ±5%, with 90% confidence. How many employment records should be
sampled?
b. They actually select a random sample of 525 employment records, and find that 229 of
the people are females. Construct the 90% confidence interval.
c. Interpret the confidence interval in this context.
d. Explain what 90% confidence means in this context.
Quiz B 9-9
e. Should representatives from the Department of Labor conclude that the percentage of
females in the U.S. labor force is lower than Europe’s rate of 46%? Explain.
f. Are the assumptions and conditions for constructing a confidence interval met?
Explain.
9-10 Chapter 9 Confidence Intervals and Hypothesis Tests for Means
Chapter 9: Sampling Distributions and Confidence Intervals for Proportions
– Quiz B – Key
Quiz B 9-11