Chapter 10: Problem 43
Step 5 of the five-step process for hypothesis testing is communication of results. What is involved in completing this step?
Chapter 10: Problem 43
Step 5 of the five-step process for hypothesis testing is communication of results. What is involved in completing this step?
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Get started for freeEvery year on Groundhog Day (February 2), the famous groundhog Punxsutawney Phil tries to predict whether there will be 6 more weeks of winter. The article "Groundhog Has Been Off Target" (USA Today, Feb. 1,2011 ) states that "based on weather data, there is no predictive skill for the groundhog." Suppose that you plan to take a random sample of 20 years and use weather data to determine the proportion of these years the groundhog's prediction was correct. a. Describe the shape, center, and spread of the sampling distribution of \(\hat{p}\) for samples of size 20 if the groundhog has only a \(50-50\) chance of making a correct prediction. b. Based on your answer to Part (a), what sample proportion values would convince you that the groundhog's predictions have a better than \(50-50\) chance of being correct?
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. \(H_{0}: p=0.05, n=75\)
Suppose that for a particular hypothesis test, the consequences of a Type I error are not very serious, but there are serious consequences associated with making a Type II error. 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.
In a hypothesis test, what does it mean to say that the null hypothesis was rejected?
The article "Poll Finds Most Oppose Return to Draft, Wouldn't Encourage Children to Enlist" (Associated Press, December 18,2005 ) reports that in a random sample of 1,000 American adults, 700 indicated that they oppose the reinstatement of a military draft. Suppose you want to use this information to decide if there is convincing evidence that the proportion of American adults who oppose reinstatement of the draft is greater than two-thirds. a. What hypotheses should be tested in order to answer this question? b. The \(P\) -value for this test is \(0.013 .\) What conclusion would you reach if \(\alpha=0.05 ?\)
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