A statistics professor wishes to estimate the average mark on a term test for a course that has multiple sections and many students. A survey of some of the students registered for the course reveals the following results: The student from the course wonders whether the population mean could have been 75 or 80.
A) Since 80 is within the 95% confidence interval, the population mean is likely to be 80.
B) Since 80 is not within the 95% confidence interval, the population mean is not likely to be 80.
C) Since 75 is within the 95% confidence interval, the population mean is likely to be 75.
D) Since neither 75 nor 80 is within the 95% confidence interval, the population mean is not likely to be 75 or 80.
E) Since 80 is not within the 95% confidence interval, the population mean is not likely to be 80, but it is likely to be 75.

Question

A statistics professor wishes to estimate the average mark on a term test for a course that has multiple sections and many students. A survey of some of the students registered for the course reveals the following results:  The student from the course wonders whether the population mean could have been 75 or 80.
A) Since 80 is within the 95% confidence interval, the population mean is likely to be 80. 
B) Since 80 is not within the 95% confidence interval, the population mean is not likely to be 80. 
C) Since 75 is within the 95% confidence interval, the population mean is likely to be 75. 
D) Since neither 75 nor 80 is within the 95% confidence interval, the population mean is not likely to be 75 or 80. 
E) Since 80 is not within the 95% confidence interval, the population mean is not likely to be 80, but it is likely to be 75.

Quizplus · Accepted Answer

Since 80 is not within the 95% confidence interval, we can reject the hypothesis that the population mean is equal to 80 at the 5% level of significance. However, we cannot reject the hypothesis that the population mean is equal to 75 at the 5% level of significance because 75 is within the 95% confidence interval. Therefore, it is not likely that the population mean is 80, but it is possible that the population mean is 75.

A Statistics Professor Wishes to Estimate the Average Mark on a Term