Question

A random sample of 50 bottles of a brand of cough syrup is selected, the alcohol content of each bottle is calculated Let μ be the average alcohol content for the population of all bottles of the brand under consideration. The resulting 95% confidence interval is (7.8,9.4) 

(a) Would a 90% confidence interval calculated from the same sample be wider or narrower? Explain. 

(b) Consider the statement: there is a 95% chance that is between 7.8 and 9.4. Is this correct? Explain. 

(c) Consider the statement: we can be highly confident that 95% of all bottles of this type of cough syrup have an alcohol content between 7.8 and 9.4. Is this correct? Explain your answer 

(d) Consider the statement: if the process of selecting a sample of size 50 and then computing the corresponding 95% confidence interval is repeated 100 times, exactly 95 of the resulting intervals will include μ. Is this correct? Explain your answer 

(e) Consider the statement: if the process of selecting a sample of size 50 and then computing the corresponding 95% confidence interval is repeated 100 times, approximately 95 of the resulting intervals will include u. Is this correct? Explain your answer.

Answer 1

(a) 90% Confidence Interval will be narrower than 95% confidence interval.

EXPLANATION: To get higher confidence, we need to make the confidence interval wider. This is evident in the multiplier,which increases with the confidence level.

(b) Correct

EXPLANATION:

The 95% confidence interval defines a range of values that we can be 95% certain contains the population mean.

(c) Not Correct.

EXPLANATION: "We can be highly confident" is to be replaced by "We are certain".

(d) Correct

EXPLANATION:

If repeated samples are taken and the 95% confidence interval is computed for each sample, 95% of the intervals will contain the population mean.

(e) Not correct

EXPLANATION:

"approximately"is to be replaced by "exactly".