*Suppose that a random sample of 50 bottles of a particular brand of cough syrup
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Question
*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 µ denote the average alcohol content for the population of all bottles of the brand under study. Suppose that the resulting 95% confidence interval is (7.8, 9.4). a. Would a 90% confidence interval calculated from this same sample have been narrower or wider than the given interval? Explain your reasoning. 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? 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 7.8 and 9.4. Is this statement correct? Why or why not? 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 µ. Is this statement correct? Why or why not?
Explanation / Answer
(a)
Critical value for 90% confidence interval is less than critical value for 95% confidence interval. So 90% confidence interval is narrower.
(b)
Yes it is true. The 95% confidence interval shows that there is 95% chance that tru population mean lie in the confidence interval.
(c)
It is incorrect.
The 95% confidence interval only provide the probability that mean lie in the interval.
(d)
yes it is true by the definition of confidence interval.
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