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c08_03.xlsx

delivery_times.xlsx

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Delivery Times at Snow Pea Restaurant
The SnowPea Restaurant is a Chinese carryout/ delivery restaurant. Most of SnowPea’s deliveries
are within a 10-mile radius, but it occasionally delivers to customers more than 10 miles away.
SnowPea employs a number of delivery people, four of whom are relatively new hires. The
restaurant has recently been receiving customer complaints about excessively long delivery times.
Therefore, SnowPea has collected data on a random sample of deliveries by its four new delivery
people during the peak dinner time. The data are in the file C08_03.xlsx. The variables are as
follows:
■
Deliverer: which person made the delivery
■
Prep Time: time from when order was placed until delivery person started driving it to
the customer
■
Travel Time: time to drive from SnowPea to customer
■
Distance: distance (miles) from SnowPea to customer
Solve the following problems and then, based on your analysis, write a report that makes
reasonable recommendations to SnowPea management.
SnowPea is concerned that one or more of the new delivery people might be slower than others.
a. Let μDi and μTi be the mean delivery time and mean total time for delivery person i, where the
total time is the sum of the delivery and prep times. Find 95% confidence intervals for each of
these means for each delivery person. Although these might be interesting, give two reasons why
they are not really fair measures for com- paring the efficiency of the delivery people.
Responding to the criticisms in part a, find a 95% confidence interval for the mean speed of
delivery for each delivery person, where speed is measured as miles per hour during the trip from
SnowPea to the customer.Then find 95% confidence intervals for the mean difference in speed
between each pair of delivery people.
2) SnowPea would like to advertise that it can achieve a total delivery time of no more than M
minutes for all customers within a 10-mile radius. On all orders that take more than M minutes,
SnowPea will give the customers a $10 certificate on their next purchase.
a. Assuming for now that the delivery people are representative of all of SnowPea’s delivery
people, find a 95% confidence interval for the proportion of deliveries (within the 10-mile limit)
that will be on time if M = 25 minutes; if M = 30 minutes; if M = 35 minutes.
b. Suppose SnowPea makes 1000 deliveries within the 10-mile limit. For each of the values of M
in part a, find a 95% confidence interval for the total dollar amount of certifi- cates it will have to
pay for being late.
3.The policy in the previous problem is simple to state and simple to administer. However, it is
somewhat unfair to customers who live close to SnowPea—they will never get $10 certifi- cates.
A fairer, but more complex, policy is the following. SnowPea first analyzes the data and finds
that total delivery times can be predicted fairly well with the equation
Predicted Delivery Time = 14.8 + 2.06*Distance
(This is based on regression analysis, the topic of Chapters 10 and 11.) Also, most of these
predic- tions are within 5 minutes of the actual delivery times.Therefore, whenever SnowPea
receives an order over the phone, it looks up the customer’s address in its computerized
geographical data- base to find distance, calculates the predicted delivery time based on this
equation, rounds
this to the nearest minute, adds 5 minutes, and guarantees this delivery time or else a $10 certificate. It does this for all customers, even those beyond the 10-mile limit.
a. Assuming again that the delivery people in the sample are representative of all of SnowPea’s
delivery people, find a 95% confidence interval for the proportion of all deliveries that will be
within the guaranteed total delivery time.
b. Suppose SnowPea makes 1000 deliveries. Find a 95% confidence interval for the total dollar
amount of certificates it will have to pay for being late.
This is fictitious data.
Order
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
Deliverer
3
1
1
3
2
2
2
3
2
1
1
2
1
1
2
3
1
1
1
2
4
3
4
1
4
2
3
1
2
4
1
2
1
3
4
2
4
3
4
1
3
2
3
Prep Time
13.0
10.9
9.2
7.2
14.5
9.5
7.1
8.5
9.8
14.3
12.0
13.0
14.9
9.7
10.0
10.8
12.1
9.9
7.9
17.2
10.2
15.0
12.5
11.0
15.7
10.1
8.2
9.2
18.7
11.0
9.3
10.1
11.4
18.0
14.0
15.4
6.1
13.9
9.5
10.3
14.4
9.4
6.6
Travel Time
30.0
17.8
9.2
14.7
21.9
8.1
31.6
29.0
4.9
13.4
12.9
8.8
8.7
29.9
18.2
22.9
5.0
9.9
9.0
6.5
29.3
24.0
19.5
10.5
29.0
2.6
19.0
13.4
8.9
9.3
22.8
14.5
26.1
10.8
28.8
21.2
6.9
21.9
17.8
9.5
29.7
23.5
17.0
Distance
13.3
8.6
4.7
4.3
12.2
3.6
11.3
10.3
2.6
5.3
4.5
4.1
4.2
11.7
9.5
8.8
1.7
4.5
3.7
3.4
3.4
9.8
5.4
5.0
7.9
1.4
7.5
7.0
5.6
2.2
8.2
7.7
12.9
3.8
11.7
10.7
2.8
8.4
4.6
4.3
6.9
12.2
6.3
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
4
2
1
1
4
1
1
1
3
4
4
4
1
4
4
4
1
3
3
3
4
3
2
2
3
2
2
1
3
1
1
1
2
15.6
9.7
14.0
11.7
12.7
14.6
9.5
7.1
8.5
9.9
14.3
12.0
13.0
16.2
10.3
8.5
9.5
13.1
8.4
17.0
14.2
8.8
12.9
10.9
9.7
13.4
8.7
17.3
7.0
9.0
13.1
11.0
12.0
18.5
13.8
5.3
3.3
0.7
1.9
12.6
7.2
7.3
26.2
28.7
23.1
12.6
28.3
9.4
29.8
21.6
10.1
24.1
6.0
18.6
13.6
29.5
17.8
23.8
18.9
7.0
16.6
31.3
3.5
11.9
11.6
7.5
5.9
9.2
2.5
1.4
0.2
0.6
6.5
3.3
3.0
5.2
8.9
7.7
7.2
8.2
4.1
13.0
11.6
3.1
5.8
2.8
2.4
4.6
14.0
6.9
6.4
10.1
2.9
9.3
8.6
1.5
4.4
3.6
3.3
Delivery Times to Snow Pea Restaurant
Part A
Delivery 1
Order
2
3
10
11
13
14
17
18
19
24
28
31
32
51
56
60
71
73
74
75
Prep Time Deliv. Time Distance
10.9
17.8
8.6
9.2
9.2
4.7
14.3
13.4
5.5
12
12.9
4.5
14.9
8.7
4.2
9.7
29.2
4.7
12.4
50
1.7
9.9
9.9
4.5
7.9
9
3.7
11
10.3
5
9.2
13.4
7
9.3
29.8
8.2
11.4
26.1
6.5
7.1
7.2
3.3
3
12.6
7.2
9.5
21.6
11.6
17.3
16.6
9.3
9
3.5
1.5
3.1
11.9
4.4
11
11.6
3.6
Delivery 2
5
6
7
9
12
15
20
26
29
32
14.5
9.5
7.1
9.8
13
10
17.2
10.1
18.7
10.1
21.9
8
31.6
4.9
8.8
18.2
6.5
9.6
8.9
14.5
12.2
3.6
11.3
12.6
4.1
9.3
3.4
1.4
5.6
7.7
40
46
47
49
50
36
42
45
66
67
69
70
76
15.4
9.4
9.7
12.9
10.9
13.4
8.7
12
21.2
23.5
13.8
29.5
17.8
18.9
7
7.5
10.7
13.2
9.2
14
6.9
10.1
2.9
3.3
1
4
8
16
22
27
34
38
41
43
52
61
62
63
65
68
72
13
7.2
8.5
10.8
15
8.2
18
13.9
14.4
6.6
8.5
13.1
8.4
17
8.8
9.7
7
30
14.7
29
22.9
24
19
10.8
21.9
29.7
17
7.3
10.1
24.1
6
13.6
23.8
31.3
13.3
4.3
10.3
8.8
9.8
7.5
3.8
8.4
6.9
6.3
3
3.1
5.8
2.8
4.6
6.4
8.6
21
23
25
30
35
37
39
44
10.2
12.5
15.7
11
14
6.1
9.5
15.6
29.3
19.5
29
9.3
28.8
6.9
17.8
18.5
3.4
5.4
7.9
2.2
11.7
2.8
4.6
5.9
n = 18
Delivery 3
Delivery 4
n = 17
48
53
54
55
57
58
59
64
12.7
9.9
14.3
12
16.2
10.3
8.5
14.2
0.7
26.2
28.7
23.1
28.3
9.4
29.8
18.6
0.2
5.2
8.9
7.7
8.2
4.1
13
2.4
S = Sqr rt (x – x- / n)
Total driving time / 25
12.788
UT sub 1 = Total delivery and prep / 25
21.317
S = sqr rt (x – x-) ^2 / n
6.896
(S) for total time = sqr rt(x-x-)^2/n = 6.6557
t sub 24 = 2.0639
12.788 +or- 2.0639 x 6.896/sqr rt (25)
12.78 +or- 2.847
CI=9.94130 thus s=2
19.68+-+36 x 2/sqr rt (37)
(19.68+-0.671)
When M=30, the total delivery time is 951.81 / 22.45 = 21.15
S=2
21.15 +- t sub 21 x 2 / sqr rt (22)
21.15 +- 2.080 x 2 / sqr rt(22)
(21.15 +- 0.8869)
When M=35, the total delivery time is 1184.41 / 52 = 22.777
22.777 +- 28 x 2 / sqr rt (52)
22.777 +- 28 x 2 / sqr rt (52)
CI=22.777 +- t sub 51 x 2/sqr rt (52)
CI=22.777+-2.021 X 2/sqr rt (52)
(22.777+-0.5605)
Total not on time:
x = 953.4 / 27 = 35.31
SD = sqr rt(x – -x/n) = 4.765
CI=35.31+- t sub n-1 x 4.765 / sqr rt(27)
35.31 +- 2.056 x 0.9170
(35.31 +- 1.880)
When M = 30
814.5 / 22 = 37.02
S=3.958
CI=37.02 +- t sub n – 1 x 3.958 / sqr rt(22)

9.9

36.1

37.02 +- 2.081 x 0.8438
(37.02 +- 1.756)
When M=35
581.8 / 15 = 38.787
SD = 3.593
CI=38.787 +- t sub n – 1 x 3.593 / sqr rt (15)
38.787 +-2.145 x 3.593 / sqr rt (15)
(38.787 +- 1.989)
95% CI for proportions of all deliveries that will be within the guaranteed time.
CI =-x +- t sub n-1 x s/sqr rt(n)
S = 2, since n>30
x-=1176/41 = 28.68
CI=28.68+- t sub 40 x 2/ sqr rt(41)
28.68 +- 2.021 x 2/sqr rt(41)
(28.68+-0.631)
If they deliver a 1000; 95%CI for the toal dollar amount of certification they will pay for 4 lates.
Total late = 1311
x- = 1311 / 35 = 37.46
CI = x- +- t sub n – 1 x 2 / sqr rt(35)
37.46+- t sub 34 x 2 / sqr rt(35)
37.46 +-2.042 x 0.3380
(37.46 +-0.69)

I would liekely advise the restaurant to use the third policy in order to encourage more customers to

10.3
14.6
11.7
14.6
9.5

9.5
5.5
3.3
1.9
12.6

4.3
2.5
1.4
0.6
6.5

6 x 60 / 17.8

l others are as follows;
Speed
28.99
30.65
23.73

20.43
28.49
23.48
26.41
27.27
24.67
28.57
31.34
13.68
18.62
27.5
30.95
18.95
29.45
28.3
27.16
29.66
22.76
25.71
33.61
32.22
34.28

MSE = 26.0341
NH = 2/(1/25) +(1/18)
20.93
S x sub 1 – x sub 2 = sqr rt (2 x 26.0341 / 20.93)
sqr rt (2.4877)
1.577
t sub 41 = 2.021
[U sub 1 – U sub 2] +- 2.021 x 1.577
[U sub 1 – U sub 2] +- 3.187
U sub 1 = 28.57
U sub 2 = 28.96
U sub 1 – U sub 2 = -0.39

CI will be [-3.577<-M sub 1 - M sub 2<- 2.797] SE = 676.52 + 351.93 = 1028.45 SE = 1028.45 / 39 = 26.371 h = 2/(1/25)+(1/16) = 19.512 qr rt ( 2x 26.371/19.512) = 11.644 .957 <- U sub 1 - U sub 4 <- 13.603] SE = 347.44 + 351.93 = 699.37 SE = 699.37 / 32 = 21.855 h = 2 / (1/18) + (1/18) = 16.94 qr rt(2 x 21.855/16.94) = 1.606 .424 <- U sub2 - U sub 4<- 13.416] ... Purchase answer to see full attachment

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