Pick-up Time Drive Time 4.94 26.96 ColumnC1, Pick-up Time, is the amount of time
ID: 3289891 • Letter: P
Question
Pick-up Time Drive Time
4.94 26.96 ColumnC1, Pick-up Time, is the amount of time (in minutes) a packaged order had
0.00 21.73 to wait to be picked up by a delivery driver.
4.98 19.74 Column C, Drive Time, is the amount of time (in minutes) required to deliver the
5.03 20.08 packaged order to the customer after it has been picked up by the driver
4.15 19.04
4.67 16.17
5.01 14.93
3.88 23.92
2.80 17.15
2.71 20.97
2.79 25.83
4.73 15.41
5.20 15.53
4.18 17.02
5.57 23.20
2.73 18.19
4.40 20.94
0.00 17.46
3.41 16.33
4.16 22.54
3.60 23.52
5.45 3.30
0.00 22.87
3.96 18.31
4.54 24.82
0.00 13.22
4.21 19.64
3.22 14.11
0.00 23.69
5.55 15.04
6.35 21.59
5.14 10.81
6.11 20.46
3.95 15.56
4.54 22.54
2.23 25.29
4.99 22.81
4.83 23.45
5.03 21.01
3.56 21.94
5.15 24.63
5.69 24.13
3.59 15.52
3.39 28.15
2.77 22.00
0.00 15.34
4.25 20.36
3.97 13.70
3.10 21.92
4.13 22.73
3.81 16.73
0.00 21.96
3.95 16.91
5.97 22.25
4.10 18.49
4.21 14.76
3.83 24.01
3.93 8.64
4.74 20.57
0.00 17.59
5.61 20.93
3.80 17.00
4.46 23.17
3.70 13.58
6.06 14.00
4.83 17.44
3.16 21.92
2.50 20.87
5.63 7.43
4.41 13.93
5.26 20.01
0.00 19.71
3.26 19.72
5.12 17.72
5.07 19.50
0.00 16.47
4.14 18.78
4.75 15.99
3.67 24.15
3.02 24.52
3.47 18.50
3.30 18.96
2.77 17.92
3.20 11.21
0.00 22.32
0.00 15.20
6.27 17.14
6.40 16.06
4.67 24.99
3.41 12.83
0.00 20.75
4.25 19.33
4.61 17.87
4.41 18.95
5.31 23.54
2.76 15.15
4.64 23.23
4.31 21.95
4.39 22.47
0.00 11.58
4.93 20.03
5.14 13.06
0.00 17.48
6.36 19.89
2.99 17.26
3.11 14.13
3.52 21.42
2.97 24.67
2.62 26.47
5.59 21.36
5.08 21.29
4.02 17.99
0.00 25.58
4.93 14.15
0.00 16.34
0.00 12.29
6.44 21.97
5.01 24.75
4.41 13.92
7.63 19.18
0.00 17.15
5.53 11.83
4.87 21.49
0.00 10.82
0.00 18.62
3.83 8.91
5.63 23.38
0.00 17.37
0.00 8.90
4.70 12.29
0.00 27.79
3.68 18.96
5.36 21.22
0.00 19.49
0.00 19.52
5.59 21.25
5.93 16.09
2.86 19.37
3.60 17.12
6.19 19.02
2.51 15.97
0.00 21.74
3.72 22.34
6.15 21.16
3.45 22.01
4.43 22.36
0.00 22.97
4.27 15.00
5.34 24.78
3.31 9.40
4.49 15.24
3.02 21.07
2.64 20.98
0.00 19.67
0.00 22.96
2.50 18.82
3.66 15.54
4.11 18.02
5.03 17.20
4.57 26.12
4.76 12.22
3.95 23.28
4.04 25.02
5.40 16.38
2.91 16.71
0.00 9.75
2.40 21.67
3.09 16.68
6.13 25.22
4.64 17.55
7.14 15.86
5.57 17.02
2.82 25.08
5.90 17.57
4.77 18.85
6.44 17.13
3.37 21.08
3.82 19.51
4.69 26.74
0.00 18.48
3.02 20.32
4.64 26.25
0.00 19.10
4.45 21.83
4.42 22.12
4.46 22.43
4.37 21.01
3.91 12.04
5.76 13.02
0.00 11.39
0.00 19.78
2.82 17.14
5.92 19.84
4.94 19.92
5.87 19.49
4.07 22.32
7.22 16.59
5.24 15.48
0.00 10.60
3.71 18.40
Wings of Fire A lite ver a year aga, Oxfod really began to grow and expand. Tony noticed that his business was beeinning to suffer Following his graduation from college, Tony Smith wanted to conwhen other fast food delivery restaurants opened around campus. tinuc to live and work in Oxford. Howcver, the community was smll and there were not a lot of readily available opportunities for a new clege graduate. Fortunately, Tony had some experiene wilh fish tacos, specially pizzas, and gourmet burgers, Most of working in the food service industry gained in the summers and throughout high school at his uncle's restaurant in Buffalo. When provided carry out and delivery as a customer convenience. How Tony decided to leverage his experience into a smal delivery and takc-out restaurant located close to the university, he thought hcneel remin competitive wih the e establishments. had hit on a great idea. Tony would ofTer a ilud are consisling of the bufTalo wings his uncle had perfeuled at his restaurant. Tonyit's free" could easily be accomplished every day except on foot called his restaurant Wings of Fire. Although success came slowly,bal Saturdays. Tony thought that if he could offer a 30-minute the uniqueness of Tony's offering coupled with the growth of the university community made Wings of Firc a success ome of these restaurants were offering guarantees such as 30 minutes or it's free." Tony's Wings of Fire now had to compcte these new restaurants, however, were dine-in establishments that ever, Tony was certain that he would need to offer a delivery guar Tony was certain that a delivery guarantee of “3() minutes or guarantee on his busiest day, he would be able to hold onto and perhaps even ermarket share r the compelition. However. Tony's business was preuy simple. Tony purchased wings locally. before he was wlng o o such a guarantee, Tony wanted The wings were then seasoned and prepared in Tony's restaurant. Once an order was received, Tony cooked the wings, which were then delivered or picked up by the customer. Tony's establishment was rders within 30 minutes of phoning them in. However, he was small and there was no place for customers to dine in the restaurant. However, his wings poved so pupular that over tie Tony hired several employees nluding three delivery drivers. Business was aged, but the delivery time might he affected by the availability steady and predictable during the week, with the biggest days being of drivers. Tony decided that he needed to analyze the opportu home football Saturdays. to ensure that it was possible to meet the 30-minute promise Tony knew it would be no problem for customers to pick up less confident about delivering orders to customers in 30 minutes or less. N only would the wings need be ooked and pack nity further.Explanation / Answer
Solution
Part (1)
Let P = Pick-up time and D = Drive time. Then, X = P + D = total time required to deliver a customer’s order.
Part (2)
To give guarantee to customers, Tony wants that on an average, X is less than 30.
We assume X ~ N(µ, 2).
To convert the above condition for guaranteeing,
Claim: Average total time required to deliver a customer’s order is less than 30 minutes.
Hypotheses:
Null H0: µ = µ0 = 30 Vs
Alternative HA: µ < 30
Part (3)
Test statistic:
t = (n)(Xbar - µ0)/s where
n = sample size
Xbar = sample mean
µ0 (given) = 30
s = sample standard deviation
Computations using Excel Functions:
n
200
Sum(X)
4504.52
Xbar
22.5226
s
4.874129
µ0
30
tcal
- 21.6954
Distribution, Critical Value and p-value
Under H0, t ~ tn - 1
Critical value = lower % point of tn - 1
p-value = P(tn – 1 < tcal)
Assuming = 0.05, tcrit = lower % point of t199 = - 1.653 and p-value = 1.23E-54
Decision Criterion (Rejection Region)
Reject H0, if tcal < tcrit or p-value < .
Decision:
Since tcal < crit, H0 is rejected. [also confirmed by p-value < ]
=> HA is accepted.
Conclusion:
There is sufficient evidence to support the claim that the average total time to deliver a customer’s order is less than 30 minutes.
DONE
Part (4)
Probability of an order taking more than 30 minutes = P(X > 30).
With sample average of 22.52 and standard deviation of 4.87,
P(X > 30) = P[Z > {(30 – 22.52)/4.87}] = P(Z > 1.5359) = 0.0623 ANSWER
Part (5)
Since probability of an order taking more than 30 minutes is just 6% and also from the conclusion of the testing above, it is recommended that Tony can give guarantee.
DONE
t = (n)(Xbar - µ0)/s where
n = sample size
Xbar = sample mean
µ0 (given) = 30
s = sample standard deviation