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Chapter 8: Q.60 (page 481)
Using the same , , and level of confidence, suppose that were instead of . Would the error bound become larger or smaller? How do you know?
Increasing the sample size causes the error bound to decrease, making the confidence interval narrower.
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What is meant by the term confident鈥� when constructing a confidence interval for a mean?
a. If we took repeated samples, approximately of the samples would produce the same confidence interval.
b. If we took repeated samples, approximately of the confidence intervals calculated from those samples would
contain the sample mean.
c. If we took repeated samples, approximately of the confidence intervals calculated from those samples would
contain the true value of the population mean.
d. If we took repeated samples, the sample mean would equal the population mean in approximately of the samples.
Construct a confidence interval for the population mean hours spent watching television per month.
(a) State the confidence interval
(b) sketch the graph, and
(c) calculate the error bound.
The Federal Election Commission (FEC) collects information about campaign contributions and disbursements for
candidates and political committees each election cycle. A political action committee (PAC) is a committee formed to raise
money for candidates and campaigns. A Leadership PAC is a PAC formed by a federal politician (senator or representative)
to raise money to help other candidates鈥� campaigns.
The FEC has reported financial information for Leadership PACs that operating during the election cycle.
The following table shows the total receipts during this cycle for a random selection of Leadership PACs.
虅
Use this sample data to construct a confidence interval for the mean amount of money raised by all Leadership PACs
during the election cycle. Use the Student's t-distribution.
A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is
approximately normal. Researchers in a hospital used the drug on a random sample of nine patients. The effective period of
the tranquilizer for each patient (in hours) was as follows:
b. Define the random variable in words.
c. Define the random variable in words.
d. Which distribution should you use for this problem? Explain your choice.
e. Construct a confidence interval for the population mean length of time.
i. State the confidence interval.
ii. Sketch the graph.
iii. Calculate the error bound.
f. What does it mean to be 鈥� confident鈥� in this problem?
The population standard deviation for the height of high school basketball players is three inches. If we want to be % confident that the sample mean height is within one inch of the true population mean height, how many randomly selected students must be surveyed?
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