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Chapter 8: Q.35 (page 479)
In one complete sentence, explain what the interval means.
The confidence interval can be interpreted as that one is confident that the true mean age for the Winter Foothill College students lies betweenyears and years.
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The American Community Survey (ACS), part of the United States Census Bureau, conducts a yearly census similar to the one taken every ten years, but with a smaller percentage of participants. The most recent survey estimates with confidence that the mean household income in the U.S. falls between . Find the point estimate for mean U.S. household income and the error bound for mean U.S. household income.
132. Public Policy Polling recently conducted a survey asking adults across the U.S. about music preferences. When asked, of the participants admitted that they have illegally downloaded music.
a. Create a confidence interval for the true proportion of American adults who have illegally downloaded music.
b. This survey was conducted through automated telephone interviews on May 6 and 7,2013. The error bound of the survey compensates for sampling error or natural variability among samples. List some factors that could affect the survey's outcome that is not covered by the margin of error.
c. Without performing any calculations, describe how the confidence interval would change if the confidence level changed from .
When designing a study to determine this population proportion, what is the minimum number you would need to survey to be confident that the population proportion is estimated to within ?
Define the random variable in words.
Suppose that an accounting firm does a study to determine the time needed to complete one person鈥檚 tax forms. It
randomly surveys 100 people. The sample mean is 23.6 hours. There is a known standard deviation of 7.0 hours. The
population distribution is assumed to be normal.
a. I. =________
ii. 蟽 =________
iii. n =________
b. In words, define the random variables X and
c. Which distribution should you use for this problem? Explain your choice.
d. Construct a 90% confidence interval for the population mean time to complete the tax forms.
i. State the confidence interval.
ii. Sketch the graph.
iii. Calculate the error bound.
e. If the firm wished to increase its level of confidence and keep the error bound the same by taking another survey,
what changes should it make?
f. If the firm did another survey, kept the error bound the same, and only surveyed 49 people, what would happen to
the level of confidence? Why?
g. Suppose that the firm decided that it needed to be at least 96% confident of the population mean length of time to
within one hour. How would the number of people the firm surveys change? Why?
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