An experiment was performed on a certain metal to determine if the strength is a function of heating time.Partial results based on a sample of 10 metal sheets are given below.The simple linear regression equation is = 1 + 1X .The time is in minutes and the strength is measured in pounds per square inch,MSE = 0.5, = 30, = 104. Determine the 95% prediction interval for the strength of a metal sheet when the average heating time is 2.5 minutes.
A)(1.68 5.32)
B)(2.94 4.06)
C)(1.78 5.22)
D)(0.78 4.22)

Question

An experiment was performed on a certain metal to determine if the strength is a function of heating time.Partial results based on a sample of 10 metal sheets are given below.The simple linear regression equation is  = 1 + 1X .The time is in minutes and the strength is measured in pounds per square inch,MSE = 0.5,  = 30,  = 104. Determine the 95% prediction interval for the strength of a metal sheet when the average heating time is 2.5 minutes.
A)(1.68 5.32) 
B)(2.94 4.06) 
C)(1.78 5.22) 
D)(0.78 4.22)

Quizplus · Accepted Answer

First, we need to calculate the standard error of estimate (SEE) using the formula:

SEE = sqrt(MSE) = sqrt(0.5) = 0.707

Next, we need to calculate the predicted strength at X=2.5 using the regression equation:

y = 1 + 1(2.5) = 3.5

Now we can calculate the 95% prediction interval using the formula:

PI = y ± t(0.025, n-2) * SEE

where t(0.025, n-2) is the t-value for a 95% confidence interval with 8 degrees of freedom (n-2 = 10-2 = 8). From a t-distribution table or calculator, we find that t(0.025, 8) = 2.306.

PI = 3.5 ± 2.306 * 0.707 = (1.78, 5.22)

Therefore, the 95% prediction interval for the strength of a metal sheet when the average heating time is 2.5 minutes is (1.78, 5.22). The best choice is C.

An Experiment Was Performed on a Certain Metal to Determine