Question

Consider the demand for Fresh Detergent in a future sales period when Enterprise Industries' price for Fresh will be x₁ = 3.70, the average price of competitors’ similar detergents will be x₂ = 3.90, and Enterprise Industries' advertising expenditure for Fresh will be x₃ = 6.50, y = the demand in hundreds of thousands of bottles. A 95 percent prediction interval for this demand is given on the following Excel add-in (MegaStat) output:

	95% Confidence Interval			95% Prediction Interval
Predicted	lower	upper		lower	upper	Leverage
8.24476	7.87935	8.61017		6.57890	9.91062	.051

(a) Find and report the 95 percent prediction interval on the output. If Enterprise Industries plans to have in inventory the number of bottles implied by the upper limit of this interval, it can be very confident that it will have enough bottles to meet demand for Fresh in the future sales period. How many bottles is this? If we multiply the number of bottles implied by the lower limit of the prediction interval by the price of Fresh ($3.70), we can be very confident that the resulting dollar amount will be the minimal revenue from Fresh in the future sales period. What is this dollar amount? (Round 95% PI to 5 decimal places and dollar amount to 1 decimal place and Level of inventory needed to the nearest whole number.)

95% PI [, ]

Level of inventory needed =  bottles.

Lower dollar amount = $

(b) Calculate a 99 percent prediction interval for the demand for Fresh in the future sales period. Hint: n = 30 and s = .791. Optional technical note needed. The distance value equals Leverage. (Round your answers to 5 decimal places.)

99% PI; [, ]

Answer 1

Solution :

a)

95% PI = [6.57890, 9.91062]

Level of inventory needed = 9.91062 * 100000 = 991062

Lower dollar amount = 6.57890 * 100000 * 3.70 = $2434193

b)

99% prediction interval = 2.779

(8.24476 + 0.051) + 2.779 *  0.791 = 10.49395

(8.24476 + 0.051) - 2.779 *  0.791 = 6.09757

99% PI = [10.49395, 6.09757]