Answered: A report described teens' attitudes…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A report described teens' attitudes about traditional media, such as TV, movies, and newspapers. In a representative sample of American teenage girls, 42% said newspapers were boring. In a representative sample of American teenage boys, 45% said newspapers were boring. Sample sizes were not given in the report. A button hyperlink to the SALT program that reads: Use SALT. (a) Suppose that the percentages reported had been based on a sample of 50 girls and 40 boys. Is there convincing evidence that the proportion of those who think that newspapers are boring is different for teenage girls and boys? Carry out a hypothesis test using ? = 0.05. (Use pgirls − pboys.) Find the test statistic. (Round your answer to two decimal places.) z = Find the P-value. (Round your answer to four decimal places.) P-value = State your conclusion. Reject H0. We do not have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring. Reject H0. We have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring. Fail to reject H0. We do not have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring. Fail to reject H0. We have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring. (b) Suppose that the percentages reported had been based on a sample of 2,200 girls and 2,400 boys. Is there convincing evidence that the proportion of those who think that newspapers are boring is different for teenage girls and boys? Carry out a hypothesis test using ? = 0.05. (Use pgirls − pboys.) Find the test statistic. (Round your answer to two decimal places.) z = Find the P-value. (Round your answer to four decimal places.) P-value = State your conclusion. Fail to reject H0. We have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring. Fail to reject H0. We do not have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring. Reject H0. We do not have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring. Reject H0. We have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring. (c) Explain why the hypothesis tests in parts (a) and (b) resulted in different conclusions. You are much less likely to get a difference in sample proportions as large as the one given when the samples are very large. You are much less likely to get a difference in sample proportions as large as the one given when the number of boys vs. girls sampled are far apart. You are much less likely to get a difference in sample proportions as large as the one given when the samples are very small. You are much less likely to get a difference in sample proportions as large as the one given when the number of boys vs. girls sampled are close together.

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