Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected and the alcohol content of each bottle is determined. Let ja denote the average alcohol content for the population of all bottles of the brand under study. Suppose that the re interval is (7.9, 9.8). (a) Would a 90% confidence interval calculated from this same sample have been narrower or wider than the given interval? Explain your reasoning. O The 90% would be wider since the z critical value for 90% is larger than the z critical value for 95%. O The 90% would be narrower since the z critical value for 90% is larger than the z critical value for 95%. • The 90% would narrower since the z criticel value for 90% is smaller then the z critical velue for 95%. O The 90% would be the same since the z critical value for 90% is the same as the z critical value for 95%. O The 90% would wider since the z critical value for 90% is smaller than the z critical value for 95%. (b) Consider the following statement: There is a 95% chance that e is between 7.9 and 9.8. Is this statement correct? Why or why not? O It is not a correct statement. There is a 5% chance that the mean is between these values. O It is not a correct stetement. Eech interval contains the mean by definition. O It is a correct statement. Each interval conteins the mean by definition. O It is a correct statement. There is only a 5% chance that the mean is not between these values. O It is not a correct statement. We are 95% confident in the general procedure for creating the interval, but the mean may or may nat be enclosed in this interval. (t) Consider the following statement: We can be highly confident that 95% of all bottles of this type of cough syrup have an alcohol content that is between 7.9 and 9.8. Is this staterment correct? Why or why not? O It is a correct staterment. This is the definition of a confidence interval. O It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for population values. O It is not a correct statement. The interval is an estimate for the population mean, not a boundary for population values. O It is a correct staterment. This interval is a great estirmate of boundaries for population values. O It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for sample values. (d) Consider the following statement: If the process of selecting a sample of size 50 and then computing the corresponding 95% interval is repeated 100 times, 95 of the resulting intervals will include u. Is this statement correct O It is not a correct statement. We expect 5 out of the 100 intervals contain the mean. O It is not a correct statement. We expect 95 out of 100 intervals will contain the mean, but we don't know this to be true. O It is a correct statement. Since we are taking the same sample, we expect all intervals to contain the mean. O It is not a correct statement. 90 out of the 100 intervals will contain the mean. O It is a correct statement. This is guaranteed by the definition confidence interval.

Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected and the alcohol content of each bottle is determined. Let ja denote the average alcohol content for the population of all bottles of the brand under study. Suppose that the re interval is (7.9, 9.8). (a) Would a 90% confidence interval calculated from this same sample have been narrower or wider than the given interval? Explain your reasoning. O The 90% would be wider since the z critical value for 90% is larger than the z critical value for 95%. O The 90% would be narrower since the z critical value for 90% is larger than the z critical value for 95%. • The 90% would narrower since the z criticel value for 90% is smaller then the z critical velue for 95%. O The 90% would be the same since the z critical value for 90% is the same as the z critical value for 95%. O The 90% would wider since the z critical value for 90% is smaller than the z critical value for 95%. (b) Consider the following statement: There is a 95% chance that e is between 7.9 and 9.8. Is this statement correct? Why or why not? O It is not a correct statement. There is a 5% chance that the mean is between these values. O It is not a correct stetement. Eech interval contains the mean by definition. O It is a correct statement. Each interval conteins the mean by definition. O It is a correct statement. There is only a 5% chance that the mean is not between these values. O It is not a correct statement. We are 95% confident in the general procedure for creating the interval, but the mean may or may nat be enclosed in this interval. (t) Consider the following statement: We can be highly confident that 95% of all bottles of this type of cough syrup have an alcohol content that is between 7.9 and 9.8. Is this staterment correct? Why or why not? O It is a correct staterment. This is the definition of a confidence interval. O It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for population values. O It is not a correct statement. The interval is an estimate for the population mean, not a boundary for population values. O It is a correct staterment. This interval is a great estirmate of boundaries for population values. O It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for sample values. (d) Consider the following statement: If the process of selecting a sample of size 50 and then computing the corresponding 95% interval is repeated 100 times, 95 of the resulting intervals will include u. Is this statement correct O It is not a correct statement. We expect 5 out of the 100 intervals contain the mean. O It is not a correct statement. We expect 95 out of 100 intervals will contain the mean, but we don't know this to be true. O It is a correct statement. Since we are taking the same sample, we expect all intervals to contain the mean. O It is not a correct statement. 90 out of the 100 intervals will contain the mean. O It is a correct statement. This is guaranteed by the definition confidence interval.

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 syrup is selected and the alcohol content of each bottle is determined. Let ja denote the average alcohol content for the population of all bottles of the brand under study. Suppose that the res interval is (7.9, 9.8). (a) Would a 90% confidence interval calculated from this same sample have been narrower wider than the given interval? Explain your reasoning. O The 90% would be wider since the z critical value for 90% is larger than the z critical value for 95%. O The 90% would be narrower since the z critical value for 90% is larger than the z critical value for 95%. • The 90% would be narrower since the z critical value for 90% is smaller than the z critical value for 95%. O The 90% would be the same since the z critical value for 90% is the same as the z critical value for 95%. O The 90% would be wider since the z critical value for 90% is smaller than the z critical value for 95%. (b) Consider the following statement: There is a 95% chance that u is between 7.9 and 9.8. Is this statement correct? Why or why not? O It is not a correct statement. There is a 5% chance that the mean is between these values. O It is not a correct stetement. Eech interval contains the mean by definition. O It is a correct statement. Each interval contains the mean by definition. O It is a corect statement. There is only a 5% chance that the mean is not between these values. O It is not a correct statement. We are 95% confident in the general procedure for creating the interval, but the mean may or may not be enclosed in this interval. (c) Consider the following statement: We can be highly confident that 95% of all bottles of this type of cough syrup have an alcohol content that is between 7.9 and 9.8. Is this statement correct? Why or why not? O It is a correct staterment. This is the definition of a confidence interval. O It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for population values. O It is not a correct statement. The interval is an estimate for the population mean, not a boundary for population values. O It is a correct statement. This interval is a great estimate of boundaries for population values. O It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for sample values. (d) Consider the following statement: If the process selecting a sample of size 50 and then computing the corresponding 95% interval is repeated 100 times, 95 of the resulting intervals will include u. Is this statement correct O It is not a correct statement. We expect 5 out of the 100 intervals to contain the mean. O It is not a correct statement. We expect 95 out of 100 intervals will contain the mean, but we don't know this to be true. O It is a correct statement. Since we are taking the same sample, we expect all intervals to contain the mean. O It is not a correct statement. 90 aut of the 100 intervals will contain the mean. O It is a correct staterment. This is guaranteed by the definition of confidence interval.

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