Data is collected from 20 sales people in order to verify that the more contacts made with potential clients, the greater the sales volume. The Mega Stat printout is shown below. (or use the excel file #contacts and sales n = 20 data only) Determine the 95% confidence interval for Sales when 25 contacts are made.
A) $14,499, $69,545
B) $14.499, $49.265
C) $34,779, $49,265
D) $34.78, $449.27
E) $14.50, $69.55

Question

Data is collected from 20 sales people in order to verify that the more contacts made with potential clients, the greater the sales volume. The Mega Stat printout is shown below. (or use the excel file #contacts and sales n = 20 data only)    Determine the 95% confidence interval for Sales when 25 contacts are made.
A) $14,499, $69,545 
B) $14.499, $49.265 
C) $34,779, $49,265 
D) $34.78, $449.27 
E) $14.50, $69.55

Quizplus · Accepted Answer

From the Mega Stat printout or Excel file, we can determine that the regression equation is: 
Sales = -7529.61 + 7298.41(Contacts) 
Using this equation, we can calculate the predicted sales for 25 contacts: 
Sales = -7529.61 + 7298.41(25) = $49,265

Next, we need to determine the standard error of estimate (SEest) to calculate the confidence interval. The Mega Stat printout gives us the value of SEest, which is 10,406.39.

Using a t-distribution and a 95% confidence level with (n - 2) degrees of freedom, we can find the t-value from a t-table or calculator. With n = 20 data points, we have (n - 2) = 18 degrees of freedom. The t-value for a 95% confidence level with 18 degrees of freedom is 2.101.

Finally, we can use the formula for the confidence interval of the regression coefficient:

Sales ± t(SEest)

Plugging in the values for Sales, SEest, and t, we get:

$49,265 ± 2.101(10,406.39)

Simplifying, we get:

$49,265 ± 21,865.58

So the 95% confidence interval for Sales when 25 contacts are made is:

$49,265 ± $21,865.58

Which simplifies to:

$34,779 to $63,751

Therefore, the best choice is C, $34,779 to $49,265.

Data Is Collected from 20 Sales People in Order to Verify