Page 400 9.34 Suppose that a random sample of 50 bottles of a particular brand o
ID: 2955703 • Letter: P
Question
Page 4009.34
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 mu denote the average alcohol content for the population of all bottles of the brand under study. Suppose that a sample of 50 results in a 95% confidence interval for mu of (7.8, 9.4).
A) Would a 90% confidence interval have been narrower or wider than the given interval? Explain your answer.
B) Consider the following statement: There is a 95% chance that mu is between 7.8 and 9.4. Is this statement correct? Why or why not?
C) Consider the following statement: If the process of selecting a sample of size 50, and then computing the corresponding 95% confidence interval is repeated 100 times, 95 of the resulting intervals will include mu. Is the statement correct? Why or why not?
Explanation / Answer
A) 90% Confidence interval will have a wider range compared to the given interval. Confidence interval is an estimate the interval likely to include the parameter given. As the confidence level increases, the range become narrower. B) This is incorrect. Confidence interval is the interval likely to include the parameter given. It is not a chance event that is affected by uncertainty. C) Consider the following statement: If the process of selecting a sample of size 50, and then computing the corresponding 95% confidence interval is repeated 100 times, 95 of the resulting intervals will include mu. Is the statement correct? Why or why not? This is correct. A 95% confidence interval indicates (95 out of 100 times) the proportion in the population that may include mu. This is an estimation of how reliable the results are.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.