A reader wrote in to the “Ask Marilyn” column in Parade magazine to say that his grandfather told him that in three-quarters of all baseball games, the winning team scores more runs in one inning than the losing team scores in the entire game. (This phenomenon is known as a “big bang.”) Marilyn responded that this proportion seemed too high to be believable. Let p be the proportion of all major-league baseball games in which a “big bang” occurs. 1. Restate the grandfather’s assertion as the null hypothesis, in symbols and in words. 2. Given Marilyn’s conjecture, state the alternative hypothesis, in symbols and in words. To investigate this claim, we randomly selected one week of the 2006 major-league baseball season, which turned out to be July 31-August 6, 2006. Then we examined the 95 games played that week to determine which had a big bang and which did not. Of the 95 games in our sample, 47 contained a big bang. 3. Is this sample proportion less than three-fourths and therefore consistent with Marilyn’s (alternative) hypothesis? 4. Calculate the test statistic and find the p-value. 5. Based on the p-value, state your conclusion with α = 0.01. In her response, Marilyn went on to conjecture that the actual proportion of “big bang” games is one-half. 6. Use a two-sided alternative, state the null and alternative hypothesis (in symbols and in words) for testing Marilyn’s claim. 7. Determine the test statistic and p-value. 8. What conclusion would you draw concerning Marilyn’s conjecture using the same α. 9. Use the sample data to produce a 95% confidence interval to estimate the proportion of all major-league baseball games that contain a big bang.

Name: A reader wrote in to the “Ask Marilyn” column in Parade magazine to sa
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Description: A reader wrote in to the “Ask Marilyn” column in Parade magazine to say that his grandfather told him that in three-quarters of all baseball games, the winning team scores more runs in one inning than the losing team scores in the entire game. (This

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section: Chapter Questions

Problem 41CT: On a game show, a contestant is given the digits 3, 4, and 5 to arrange in the proper order to form...

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A reader wrote in to the “Ask Marilyn” column in Parade magazine to say that his grandfather told him that in three-quarters of all baseball games, the winning team scores more runs in one inning than the losing team scores in the entire game. (This phenomenon is known as a “big bang.”) Marilyn responded that this proportion seemed too high to be believable. Let p be the proportion of all major-league baseball games in which a “big bang” occurs. 1. Restate the grandfather’s assertion as the null hypothesis, in symbols and in words. 2. Given Marilyn’s conjecture, state the alternative hypothesis, in symbols and in words. To investigate this claim, we randomly selected one week of the 2006 major-league baseball season, which turned out to be July 31-August 6, 2006. Then we examined the 95 games played that week to determine which had a big bang and which did not. Of the 95 games in our sample, 47 contained a big bang. 3. Is this sample proportion less than three-fourths and therefore consistent with Marilyn’s (alternative) hypothesis? 4. Calculate the test statistic and find the p-value. 5. Based on the p-value, state your conclusion with α = 0.01. In her response, Marilyn went on to conjecture that the actual proportion of “big bang” games is one-half. 6. Use a two-sided alternative, state the null and alternative hypothesis (in symbols and in words) for testing Marilyn’s claim. 7. Determine the test statistic and p-value. 8. What conclusion would you draw concerning Marilyn’s conjecture using the same α. 9. Use the sample data to produce a 95% confidence interval to estimate the proportion of all major-league baseball games that contain a big bang.

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