Suppose that a random sample of 50 bottles of a particular brand of cough medicine is selected and the alcohol content of each bottle is determined. Let u denote the mean alcohol content (in percent) for the population of all bottles of the brand under study. Suppose that the sample of 50 results in a 95% confidence interval for u of (7.8, 9.4). (a) Would a 90% confidence interval have been narrower or wider than the given interval? Explain your answer. A 90% confidence interval would have been ---Select--- than the 95% confidence interval. We ---Select--- ✓values we decrease confidence. (b) Consider the following statement: There is a 95% chance that is between 7.8 and 9.4. Is this statement correct? Why or why not? The statement ---Select--- correct. The population mean, μ, ---Select--- , and therefore we ---Select--- talk about the probability that it falls within a certain interval. (c) Consider the following statement: If the process of selecting a random sample of size 50 and then computing the corresponding 95% confidence interval is repeated 100 times, 95 of the resulting intervals will include u. Is this statement correct? Why or why not? The statement --Select--- correct. We can ---Select--- ✓95 out of every 100 samples will result in confidence intervals that will contain μ.

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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Transcribed Image Text:Suppose that a random sample of 50 bottles of a particular brand of cough medicine is selected and the alcohol content of each bottle is determined. Let u denote the mean alcohol content (in percent) for the population of all bottles of the brand under study. Suppose that the sample of 50 results in a 95% confidence interval for u of (7.8, 9.4). μ (a) Would a 90% confidence interval have been narrower or wider than the given interval? Explain your answer. A 90% confidence interval would have been | ---Select--- than the 95% confidence interval. We ---Select--- values if we decrease confidence. (b) Consider the following statement: There is a 95% chance that μ is between 7.8 and 9.4. Is this statement correct? Why or why not? The statement |---Select--- correct. The population mean, u, ---Select--- ✓ and therefore we [---Select--- talk about the probability that it falls within a certain interval. (c) Consider the following statement: If the process of selecting a random sample of size 50 and then computing the corresponding 95% confidence interval is repeated 100 times, 95 of the resulting intervals will include u. Is this statement correct? Why or why not? The statement ---Select--- correct. We can ---Select--- 95 out of every 100 samples will result in confidence intervals that will contain μ.

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