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Chapter 10: Problem 27
Describe the two types of errors that might be made when a hypothesis test is carried out.
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According to a survey of 1,000 adult Americans conducted by Opinion Research Corporation, 210 of those surveyed said playing the lottery would be the most practical way for them to accumulate \(\$ 200,000\) in net wealth in their lifetime ("One in Five Believe Path to Riches Is the Lottery," San Luis Obispo Tribune, January 11,2006 ). Although the article does not describe how the sample was selected, for purposes of this exercise, assume that the sample is a random sample of adult Americans. Suppose that you want to use the data from this survey to decide if there is convincing evidence that more than \(20 \%\) of adult Americans believe that playing the lottery is the best strategy for accumulating \(\$ 200,000\) in net wealth. a. What hypotheses should be tested in order to answer this question? b. The \(P\) -value for this test is 0.215 . What conclusion would you reach if \(\alpha=0.05 ?\)
Suppose that for a particular hypothesis test, the consequences of a Type I error are very serious. Would you want to carry out the test using a small significance level \(\alpha\) (such as 0.01 ) or a larger significance level (such as 0.10 )? Explain the reason for your choice.
USA Today (March 4, 2010) described a survey of 1,000 women ages 22 to 35 who work full time. Each woman who participated in the survey was asked if she would be willing to give up some personal time in order to make more money. To determine if the resulting data provided convincing evidence that the majority of women ages 22 to 35 who work full time would be willing to give up some personal time for more money, what hypotheses should you test?
Assuming a random sample from a large population, for which of the following null hypotheses and sample sizes is the large-sample \(z\) test appropriate? a. \(H_{0}: p=0.2, n=25\) b. \(H_{0}: p=0.6, n=200\) c. \(H_{0}: p=0.9, n=100\) d. \(H_{0}: p=0.05, n=75\)
The article "Theaters Losing Out to Living Rooms" (San Luis Obispo Tribune, June 17,2005 ) states that movie attendance declined in \(2005 .\) The Associated Press found that 730 of 1,000 randomly selected adult Americans prefer to watch movies at home rather than at a movie theater. Is there convincing evidence that a majority of adult Americans prefer to watch movies at home? Test the relevant hypotheses using a 0.05 significance level.
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