Question

You are the manager of a beer distribution center and you want to determine a method for allocating beer delivery costs to the customers. Although one cost clearly relates to travel time within a particular route, another variable cost reflects the time required to unload the cases of beer at the delivery point. You want to develop a model to predict this cost, so you collect a random sample of 20 deliveries within your territory. The unloading time and the number of cases are shown in the Excel data file for this assignment, under the tab Delivery.

i. Construct a 95% confidence interval estimate of the mean time to unload 150 cases of beer and a 95% prediction interval of the unloading time for a single delivery of 150 cases of beer. Explain your results.

j. What conclusions can you reach from the analysis above regarding the relationship between unloading time and the number of cases of beer delivered?

k. If your delivery cost is $100 per hour, what variable cost for unloading 150 cases of beer should you add to that customers invoice?   Explain your thought process.

Customer	Number of Cases	Delivery Time
1	52	32.1
2	64	34.8
3	73	36.2
4	85	37.8
5	95	37.8
6	103	39.7
7	116	38.5
8	121	41.9
9	143	44.2
10	157	47.1
11	161	43
12	184	49.4
13	202	57.2
14	218	56.8
15	243	60.6
16	254	61.2
17	267	58.2
18	275	63.1
19	287	65.6
20	298	67.3

Answer 1

Minitab output:

Regression Analysis: Delivery Time versus Number of Cases

The regression equation is
Delivery Time = 24.8 + 0.140 Number of Cases

Predictor Coef SE Coef T P
Constant 24.835 1.054 23.56 0.000
Number of Cases 0.140026 0.005627 24.88 0.000

S = 1.98650 R-Sq = 97.2% R-Sq(adj) = 97.0%

Analysis of Variance

Source DF SS MS F P
Regression 1 2443.5 2443.5 619.20 0.000
Residual Error 18 71.0 3.9
Total 19 2514.5

Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI
1 45.838 0.458 (44.876, 46.801) (41.555, 50.121)

Values of Predictors for New Observations

Number
New Obs of Cases
1 150

i. 95% confidence interval estimate of the mean time to unload 150 cases of beer: (44.876, 46.801)

i.e. we are 95% confident that the mean time to unload 150 cases of beer lies in  (44.876, 46.801).

95% prediction interval of the unloading time for a single delivery of 150 cases of beer: (41.555, 50.121).

we are 95% confident that the unloading time for a single delivery of 150 cases of beer lies in (41.555, 50.121).

j. Since from ANOVA table we see that p-value of F test <0.05 so there is sufficient evidence to conclude that there is significant linear relationship between unloading time and the number of cases of beer delivered. Moreover since R-Sq = 97.2% so 97.2% of total variation in the sample of unloading time is explained by this regression line.

k.  If your delivery cost is $100 per hour, variable cost for unloading 150 cases of beer=45.838*100=$4583.8