Consider the demand for Fresh Detergent in a future sales period when Enterprise

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. A 95 percent prediction interval for this demand is given on the following Excel add-in (MegaStat) output:

(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.)

(b) Calculate a 99 percent prediction interval for the demand for Fresh in the future sales period. Hint: n = 30 and s = .716. Optional technical note needed. The distance value equals Leverage. (Round your answers to 5 decimal places.)

99% PI; [, ]

95% Confidence Interval 95% Prediction Interval Predicted lower upper lower upper Leverage 8.48532 8.11830 8.85233 6.96891 10.00172 .062

Explanation / Answer

(a) In the question, the prediction interval for the demand is given as-

Part 1 - Prediction Interval (6.96891, 10.00172), this implies that the future predicted demand lies in this range with 95% confidence.

Part 2 - Level of inventory needed is 10 if we round off the upper value of prediction interval of demand to a whole number.

Part 3 - Minimum Revenue - 6.96891, the lower value of prediction interval rounded off to 7 and multiplied by 3.70 as the future price of Fresh detergent.

= 7*3.70

=25.9 dollars.

(b) Given n = 30 and s = 0.716

Predition Interval is given by -

Predicted value of demand +- (t value for alpha 0.01 two tail test and df =29)*s

df = n-1

Hence,

8.48532+-(2.756*0.716)

=8.48532+-1.973296

=(6.51202, 10.45862)

Ans. 99% Predition Interval of demand is (6.51202, 10.45862)

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---