THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The faculty advisor at a local business school is interested in determining the monthly expenditures on stationeries for students.The advisor samples some students from each class and computes the sample mean and standard deviation for each class.

-Find a 98% confidence interval for the mean monthly expenditures.
A)64.67 ± 5.285
B)64.67 ± 3.278
C)64.67 ± 7.875
D)64.67 ± 4.326

Question

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The faculty advisor at a local business school is interested in determining the monthly expenditures on stationeries for students.The advisor samples some students from each class and computes the sample mean and standard deviation for each class.
 
-Find a 98% confidence interval for the mean monthly expenditures.
A)64.67 ± 5.285 
B)64.67 ± 3.278 
C)64.67 ± 7.875 
D)64.67 ± 4.326

Quizplus · Accepted Answer

A 98% confidence interval corresponds to a level of significance of 0.02/2 = 0.01 in each tail of the normal distribution. Using a t-distribution with n-1 degrees of freedom (where n is the sample size), the critical value for a 98% confidence interval with 30 degrees of freedom (chosen based on the sample size) is 2.457. The margin of error is equal to the critical value times the standard error, which is equal to the standard deviation divided by the square root of the sample size. Therefore, the margin of error is 2.457*(5.568/sqrt(30)) = 3.278. The 98% confidence interval is then 64.67 ± 3.278, which is answer choice B.