Question

Bill Smith is the new Marketing Director at the Jonesfield Ham Company. In the interest of assessing Jonesfield’s pricing policy, Bill examined sales data for the last 24 months, and estimated the following relationship

Q = 125 - 10P + 5Ps + 4I
(15) (2.8) (3.2) (3.6)
R² = .75, SER = 2. 5
Where Q number of sugar cured hams sold in the Richmond area per mont
P price per pound of the hams
Ps price per point of Smithfield salt-cured country hams
I Per capita income (in thousands of dollars.)
Assume that at present P = $3.00; Ps = $5.00, I = $15 (000).
Using current values, provide an approximate 95% confidence interval for forecasted sales.
a. 175.00 to 185.00
b. 177.50 to 182.50
c. 179.25 to 180.75
d. 178.50 to 181.50

Answer 1

The calculation of the 95% confidence interval for forecasted sales requires additional statistical information not provided in the question, typically involving the standard error of the estimate and the t-distribution. Without it, exact computation is not possible.

Step-by-step explanation:

The question involves using the estimated sales relationship to find the 95% confidence interval for forecasted sales of sugar cured hams. This calculation would normally require using the standard error of the estimate (SER) and the t-distribution. However, the values given in the question do not provide enough information to use the t-distribution correctly, as we would need to know the degrees of freedom. Therefore, it may not be possible to calculate an exact confidence interval without additional information.

If we approximate using available data, plugging the current values of P, Ps, and I into the estimated relationship, you would first compute the estimated sales (Q) and then create an interval around this estimate using the SER in a range that would typically cover 95% of possible outcomes. However, the student should be advised that such a calculation without using the appropriate factors from the t-distribution may not accurately represent a true 95% confidence interval.

Therefore, the correct way to approach this would be to use the regression model Q = 125 - 10P + 5Ps + 4I, plugging in P = $3.00, Ps = $5.00, and I = $15, to find the forecasted sales and then calculate the interval using an appropriate statistical technique, assuming that the correct parameters for the confidence interval calculation are available.