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Chapter 7: Problem 91
A poll on a proposition showed that we are \(95 \%\) confident that the population proportion of voters supporting it is between \(40 \%\) and \(48 \%\). Find the margin of error.
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The mean weight of all professional NBA basketball players is \(218.8\) pounds. A sample of 50 professional basketball players has a mean weight of \(217.6\) pounds. Which number is \(\mu\), and which number is \(\bar{x}\) ?
According to a 2017 Gallup poll, 572 out of 1021 randomly selected smokers polled believed they are discriminated against in public life or in employment because of their smoking. a. What percentage of the smokers polled believed they are discriminated against because of their smoking? b. Check the conditions to determine whether the CLT can be used to find a confidence interval. c. Find a \(95 \%\) confidence interval for the population proportion of smokers who believe they are discriminated against because of their smoking. d. Can this confidence interval be used to conclude the majority of Americans believe smokers are discriminated against because of their smoking? Why or why not?
According to The Washington Post, \(72 \%\) of high school seniors have a driver's license. Suppose we take a random sample of 100 high school seniors and find the proportion who have a driver's license. a. What value should we expect for our sample proportion? b. What is the standard error? c. Use your answers to parts a and \(\mathrm{b}\) to complete this sentence: We expect _____\(\%\) to have their driver's license, give or take ____\(\%\). d. Suppose we increased the sample size from 100 to 500 . What effect would this have on the standard error? Recalculate the standard error to see if your prediction was correct.
Assume your class has 30 students and you want a random sample of 10 of them. Describe how to randomly select 10 people from your class using the random number table.
According to a 2018 Rasmussen Poll, \(40 \%\) of American adults were very likely to watch some of the Winter Olympic coverage on television. The survey polled 1000 American adults and had a margin of error of plus or minus 3 percentage points with a \(95 \%\) level of confidence. a. State the survey results in confidence interval form and interpret the interval. b. If the Rasmussen Poll was to conduct 100 such surveys of 1000 American adults, how many of them would result in confidence intervals that included the true population proportion? c. Suppose a student wrote this interpretation of the confidence interval: "We are \(95 \%\) confident that the sample proportion is between \(37 \%\) and \(43 \%\)." What, if anything, is incorrect in this interpretation?
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