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Chapter 8: Q.1.3 (page 476)
True or false: The interval from to has a chance of containing the actual population standard deviation . Justify your answer.
The provided statement is false.
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Refer to Exercise . As Gallup indicates, the percentage point margin of error for this poll includes only sampling variability (what they call “sampling error”). What other potential sources of error (Gallup calls these “non-sampling errors”) could affect the accuracy of the estimate?
65. Critical value What critical valuefrom Table would you use for a confidence interval for the population mean based on an SRS of size ? If possible, use technology to find a more accurate value of . What advantage does the more accurate provide?
In each of the following situations, discuss whether it would be appropriate to construct a one-sample interval to estimate the population mean.
(a) We collect data from a random sample of adult residents in a state. Our goal is to estimate the overall percentage of adults in the state who are college graduates.
(b) The coach of a college men’s basketball team records the resting heart rates of the team members. We use these data to construct a confidence interval for the mean resting heart rate of all male students at this college.
(c) Do teens text more than they call? To find out, an AP Statistics class at a large high school collected data on the number of text messages and calls sent or received by each of randomly selected students. The Fathom boxplot below displays the difference (texts calls) for each student.
Prayer in school A New York Times/CBS News Poll asked the question, “Do you favor an amendment to the Constitution that would permit organized prayer in public schools?” Sixty-six percent of the sample answered “Yes.” The article describing the poll says that it “is based on telephone interviews conducted from Sept. 13 to Sept. 18 with adults around the United States, excluding Alaska and Hawaii. . . . The telephone numbers were formed by random digits, thus permitting access to both listed and unlisted residential numbers.” The article gives the margin of error for a confidence level as percentage points.
(a) Explain what the margin of error means to someone who knows little statistics.
(b) State and interpret the 95% confidence interval.
(c) Interpret the confidence level.
Got shoes? The class in Exercise 1 wants to estimate the variability in the number of pairs of shoes that female students have by estimating the population variance .
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