The following data is available of estimated overhead costs using linear regression:
Table of Selected Values: t Distribution

What is the interval around Y if 95 percent confidence is desired?
A) Y $\pm$ 20.024
B) Y $\pm$ 43.87759
C) Y $\pm$ 52.8133
D) Y $\pm$ 53.33893

Question

The following data is available of estimated overhead costs using linear regression:  
Table of Selected Values: t Distribution

What is the interval around Y if 95 percent confidence is desired?
A) Y $\pm$ 20.024 
B) Y $\pm$ 43.87759 
C) Y $\pm$ 52.8133 
D) Y $\pm$ 53.33893

Quizplus · Accepted Answer

The interval around Y would be Y ± tα/2 * SE where tα/2 is the critical value for a 95% confidence interval with n-2 degrees of freedom (n=sample size). From the table given, the value of tα/2 for n-2=21-2=19 degrees of freedom and a 95% confidence interval is 2.093. The SE (standard error) is given as 20.024. Therefore, the interval around Y would be Y ± 2.093 * 20.024 = Y ± 41.881. Plugging in the values given in the answer choices, we see that only option D, Y ± 53.33893, falls within this interval. Therefore, the answer is D.

The Following Data Is Available of Estimated Overhead Costs Using ±\pm±

The Following Data Is Available of Estimated Overhead Costs Using $\pm$