Question

An SRS yields a sample mean, x ̅, of 8.6. A 90% confidence interval from the same data is 8.6 ± 2.4. Which of the following statements is true about the situation?

(A)   If the population mean were 5.2, the sample mean of 8.6 would be highly likely.

(B)   If the population mean were 5.2, the sample mean of 8.6 would be highly unlikely.

(C)   There is a 90% chance that the population mean lies between 6.2 and 11.0

(D)   If this procedure were repeated many times, 90% of the sample means would fall between 6.2 and 11.

(E)   90% of the sample data lie between 6.2 and 11

Answer 1

The Confidence interval provides the confidence that the population parameter will lie in this range with certain level of confidence. We can interpret the 95% confidence interval as if we repeat sampling 100 times then the 95 times true parameter will lie within the obtained confidence interval.

In the given question, we have sample mean = 8.6 and a 90% Confidence Interval is 8.6 ± 2.4

For given data the lower limit is 6.2 and upper limit is 11, hence as per the definition of Confidence interval, if we repeat sampling procedure many times, 90% of the sample mean will fall between 6.2 and 11.

Hence the correct option is (D) If this procedure were repeated many times, 90% of the sample means would fall between 6.2 and 11.