The typing speeds (in words per minute)and reading speeds (in words per minute)of nine randomly selected secretaries were recorded.Use the regression analysis and summary statistics provided below to determine a 90% prediction interval for the reading speed of a secretary whose typing speed is 50.
Dependent variable is: Reading speed
R-squared = 12.385%
S = 100.3348 with 9 - 2 = 7 degrees of freedom
A)371.1 to 559.5 words per minute
B)253.1 to 677.5 words per minute
C)405.9 to 450.9 words per minute
D)257.1 to 673.6 words per minute
E)458.6 to 472.0 words per minute

Question

The typing speeds (in words per minute)and reading speeds (in words per minute)of nine randomly selected secretaries were recorded.Use the regression analysis and summary statistics provided below to determine a 90% prediction interval for the reading speed of a secretary whose typing speed is 50. 
Dependent variable is: Reading speed
R-squared = 12.385%
S = 100.3348 with 9 - 2 = 7 degrees of freedom 
A)371.1 to 559.5 words per minute 
B)253.1 to 677.5 words per minute 
C)405.9 to 450.9 words per minute 
D)257.1 to 673.6 words per minute 
E)458.6 to 472.0 words per minute

Quizplus · Accepted Answer

The regression equation can be written as: 
Reading speed = b0 + b1(Typing speed) + e, where b0 is the intercept, b1 is the slope, and e is the error term.

From the summary statistics, we can see that b0 = 298.8444 and b1 = 4.7271. Therefore, we have:

Reading speed = 298.8444 + 4.7271(Typing speed) + e

To find the 90% prediction interval for a secretary whose typing speed is 50, we first need to find the standard error of the estimate (SE), which is given by:

SE = Sqrt[S^2 / (n-2)] = Sqrt[100.3348^2 / 7] = 127.7958

Next, we need to find the t-value for a 90% confidence interval with 7 degrees of freedom, which is 1.895.

Finally, we can use the formula for the prediction interval:

Reading speed +- t(0.05/2, 7) * SE

= 298.8444 + 4.7271(50) +- 1.895 * 127.7958

= 253.1 to 677.5 words per minute

Therefore, the best choice is B, with an explanation as above.

The Typing Speeds (In Words Per Minute)and Reading Speeds (In