Moe’s Southwest Grill and Postmates.com Assignment You have been asked to evalua

Question

Moe’s Southwest Grill and Postmates.com

Assignment

           

            You have been asked to evaluate the program and make suggestions.

Please address the following questions. Put the answers to the following questions into a one to two page report.

a) What is the average total delivery time?

b) The company’s goal is to have 95% of all orders delivered within 26 minutes. Conduct the appropriate statistical test to see if you think this is possible.

c) Does it take significantly more time for delivery on weekends than weekdays?

Day Time Assemble Wait Deliver Distance 5 4 14.86 3.08 6.02 2.5 5 5 14.84 13.81 5.47 3.3 5 6 15.41 9.91 8.99 4.9 5 7 16.34 2.08 7.98 3.8 5 8 15.19 2.69 9.01 4.9 5 9 16.32 0.29 10.86 5.3 5 10 15.32 4.12 6.31 2.9 5 11 14.06 0.27 7.87 3.5 6 4 15.6 11.35 12.47 6.4 6 5 15.16 11.98 7.58 3.5 6 6 14.37 0.36 10.65 5.1 6 7 14.24 1.21 7.83 3.7 6 8 16.17 4.32 6.75 3.6 6 9 15.48 1.54 9.59 5.2 6 10 14.56 0.13 6.99 3.4 6 11 11.65 2.67 8.94 4.8 7 4 15.6 0.78 8.38 3.7 7 5 15.65 0.84 5.62 2.4 7 6 16.59 3.36 5.67 3.1 7 7 14.51 6.05 9.18 4.4 7 8 14.8 1.14 5.04 2.2 7 9 17.02 1.35 8.16 3.8 7 10 12.89 0.2 6.81 3.5 7 11 14.53 1.25 3.71 1.7 1 4 15.01 0.8 6.44 2.5 1 5 13.5 5.47 7.98 4.1 1 6 14.61 9.74 5.85 2 1 7 15.48 0.58 4.72 1.9 1 8 15.99 0.44 7 3.6 1 9 13.87 0.06 8.52 3.6 1 10 14.71 1.21 8.48 3.9 1 11 13.22 0.3 6.61 3.3 2 4 14.45 0.04 8.98 4.4 2 5 14.77 6.8 7.93 3.9 2 6 12.93 0.66 10.31 4.8 2 7 16.18 13 4.86 2.1 2 8 14.99 1.37 8.9 4.7 2 9 14.13 3.51 8.78 4.6 2 10 17.02 2.27 6.27 3.3 2 11 15.51 0.16 8.83 3.7 3 4 14.74 0.51 7.54 3.6 3 5 15.59 0.88 10.49 5.8 3 6 15.46 0.54 8.33 4.2 3 7 15.3 2.55 7.76 3.6 3 8 14.52 1.31 8.88 4 3 9 15.27 1.28 7.17 4 3 10 14.65 0.4 8.98 4.4 3 11 15.58 0.13 7.06 3.8 4 4 15.69 0.21 9.86 4.9 4 5 16.54 2.16 5.71 2.8 4 6 13.81 0.1 7.12 4 4 7 15.74 1.26 6.08 3.1 4 8 13.68 0.7 7.91 4 4 9 15.54 0.32 6.05 3.3 4 10 14.15 2.18 5.91 2.7 4 11 14.13 1.19 7.53 4.1 5 4 15.07 0.69 6.31 3.3 5 5 16.05 2.44 7.37 3.9 5 6 12.63 3.42 4.27 2.1 5 7 14.8 3.04 7.87 4.4 5 8 14.84 0.37 7.11 3.8 5 9 16.27 2.77 7.28 3.5 5 10 15.14 1.51 9.83 4.8 5 11 14.12 3.04 6.28 2.9 6 4 13.97 4.17 5.83 3 6 5 16.27 1.27 5.5 2.9 6 6 13.45 2.49 8.89 4.3 6 7 14.98 4.46 7.08 3.8 6 8 15.36 0.28 5.57 2.8 6 9 12.56 2.46 7.83 4.4 6 10 14.1 4.16 7.74 3.4 6 11 16.06 4.41 11.29 5.3 7 4 14.64 0.44 8.72 3.9 7 5 16.24 10.5 6.31 3.5 7 6 16.16 0.92 9.69 4.9 7 7 15.98 6.42 10.02 4.9 7 8 15.55 0.52 11.41 5.7 7 9 12.95 1.15 5.87 2.9 7 10 14.07 0.67 6.64 3.2 7 11 14.15 0.4 9.65 5.2 1 4 14.71 0.2 10.88 5 1 5 15.46 6.67 6.43 3.2 1 6 14.06 2.12 6.71 2.9 1 7 14.25 0.83 4.12 2.2 1 8 13.81 0.63 8.88 4.6 1 9 15.28 3.77 5.86 2.7 1 10 12.99 1.92 10.74 6.1 1 11 15.58 0.94 5.83 2.4 2 4 14.35 0.85 8.25 3.4 2 5 14.32 1.61 6.93 3.8 2 6 13.34 0.58 7.81 3.9 2 7 16.49 5.07 9.33 5 2 8 16.49 0.99 6.04 3.2 2 9 15.96 0.17 5.6 3 2 10 15.98 0.02 7.04 3.2 2 11 15.71 0.21 9.41 4.9 3 4 15.35 1.63 10.93 5.1 3 5 13.15 6.96 8.14 4.1 3 6 14.97 1.48 6.46 3.2 3 7 14.13 4.83 7.79 3.9 3 8 16 0.55 7.06 3.1 3 9 12.49 0.14 4.27 2.3 3 10 14.19 0.72 8.87 4.5 3 11 15.33 0.2 10.19 4.9 4 4 16.53 1.18 8.14 4.8 4 5 14.18 0.82 7.91 4.5 4 6 15.68 0.04 8.28 4.7 4 7 15.64 0.2 4.85 2.5 4 8 14.34 1.43 8.02 3.7 4 9 15.01 0.6 9.36 5.6 4 10 15.72 0.19 8.52 3.8 4 11 14.68 0.44 7.35 2.7 5 4 14.88 11.11 7.59 4 5 5 15.42 1.7 8.33 3.8 5 6 15.73 1.02 11.22 5.9 5 7 15.09 2.12 5.97 2.6 5 8 15.45 0.52 8.28 4.2 5 9 15.24 1.75 6.63 3 5 10 13.52 8.82 9.56 4.9 5 11 14.29 8.07 6.7 3.8 6 4 16.48 1.49 5.83 2.6 6 5 14.82 8.81 6.02 3 6 6 15.64 4.68 6.47 2.6 6 7 13.96 2.72 8.16 4.3 6 8 16.03 3.11 6.55 3.9 6 9 16.81 13.32 7.17 3.4 6 10 15.69 1.5 8.62 4.3 6 11 15.91 3.94 8.81 4.2 7 4 13.58 0.11 9.62 4.6 7 5 14.85 0.18 9.39 4.6 7 6 14.55 2.36 4.88 2.5 7 7 14.59 0.27 9.21 4.7 7 8 14.39 1.22 5.18 2 7 9 14.52 1.43 9.17 4.7 7 10 16.18 0.86 7.78 4.3 7 11 14.52 0.97 10.49 5.1 1 4 15.6 1.02 4.91 2.4 1 5 14.08 0.25 8.54 4.3 1 6 17.43 11.38 4.07 1.2 1 7 13.92 1.07 5.88 3.7 1 8 15.07 0.17 7.09 3.5 1 9 14.26 1.97 5.8 2.6 1 10 15.19 0.19 7.03 3.4 1 11 14.69 1.01 7.94 3.9 2 4 15.18 1.04 8.45 4 2 5 16.06 6.78 6.59 2.8 2 6 12.81 1.33 10.75 5.4 2 7 14.33 2.43 8.68 3.6 2 8 15.27 0.49 6.05 3 2 9 12.96 0.44 8.3 4.2 2 10 14.93 1.04 8.53 3.7 2 11 15.28 0.03 5.96 2.7 3 4 16.25 0.9 8.2 3.2 3 5 16 0.32 5.67 3.2 3 6 14.44 2.38 8.85 4.6 3 7 14.13 0.07 9.02 4.5 3 8 15.78 0.41 6.65 3.5 3 9 13.69 0.47 10.36 5.1 3 10 16.05 0.71 7.9 4.4 3 11 14.42 0.65 8.51 4.3 4 4 14.78 0.28 7.73 4.1 4 5 16.26 0.66 9.24 4.3 4 6 16.7 0.85 9.91 5.1 4 7 14.37 0.58 5.85 2.4 4 8 15.87 0.5 4.68 3.1 4 9 14.85 0.07 8.47 4.6 4 10 14.8 0.63 9.02 4.9 4 11 16.48 0.38 10.57 5.2 5 4 13.14 4.02 10.71 5.2 5 5 13.54 4.01 3.52 1.9 5 6 15.01 1.83 10.56 5.8 5 7 13.67 0.63 5.09 2.7 5 8 16.49 3.63 8.47 4.2 5 9 14.94 0.96 6.81 3.4 5 10 14.86 4.99 10.84 5.5 5 11 14.01 7.64 6.47 3.4 6 4 13.73 0.48 7.33 3.5 6 5 14.89 5.65 8.82 4.6 6 6 15.84 0.74 9.34 4.3 6 7 15.99 8.32 8.24 3.9 6 8 16.17 1.75 7.54 4.1 6 9 15.64 15.15 9.43 5.2 6 10 14.13 0.14 11.21 5.5 6 11 14.62 11.19 10.67 5.9 7 4 16.83 0.23 7.7 3.7 7 5 15.44 10.14 6.37 2.8 7 6 13.27 1.86 8.14 3.7 7 7 16.43 2.13 8.22 3.8 7 8 15.55 0.18 9.41 4 7 9 14.47 3.32 6.62 3.1 7 10 15.09 0.49 4.83 3 7 11 16.57 0.04 6.55 3.2 1 4 13.95 1.46 3.12 1.7 1 5 13.98 1.01 7.19 3.3 1 6 13.76 4.56 9.39 5 1 7 16.48 1.31 6.9 2.9 1 8 15.78 2.18 8.29 3.7 1 9 14.42 0.24 11.85 5.8 1 10 15.76 4.19 8.83 4.6 1 11 13.87 0.08 3.92 2.3 2 4 16.45 0.16 12.25 5.5 2 5 13.58 1 9.9 5.3 2 6 13.25 8.7 8.68 4.1 2 7 16.02 0.88 8.97 4 2 8 13.75 0.22 9.56 4.7 2 9 14.4 1.14 8.65 4.6 2 10 13.85 0.39 10.49 5.3 2 11 13.5 0.16 6.87 3 3 4 15.34 0.7 4.86 2.5 3 5 16.79 0.94 11.14 6.1 3 6 15.46 0.66 8.76 4.6 3 7 14.42 6.14 9.41 4.4 3 8 14.65 3.31 3.93 2.5 3 9 14.76 2 9.98 4.2 3 10 13.6 1.91 6.32 3.3 3 11 14.24 1.19 9.4 4.5 4 4 15.7 1.77 6.54 3.3 4 5 15.51 4.83 8.45 4.2 4 6 14.05 0.68 5.3 2.5 4 7 15.6 3.5 6.96 3.6 4 8 15.54 1.73 6.88 2.9 4 9 13.49 1.29 8.22 4.7 4 10 15.46 1.49 8.06 4.1 4 11 15.58 0.31 12.55 6.4 5 4 14.06 1.33 9 4.7 5 5 15.53 2.2 8.25 4.1 5 6 15.94 2.27 12.58 6.4 5 7 15.08 8.31 9.63 5 5 8 15.46 1.61 10.42 5 5 9 15.73 3.45 7.69 3.8 5 10 15.21 7.22 7.88 4 5 11 13.3 3.57 7.43 3.6 6 4 14.14 5.94 6.56 3.1 6 5 14.59 1.1 4.72 2.9 6 6 15.77 2.14 8.58 4.9 6 7 12.64 8.2 8.83 5.1 6 8 16.69 21.66 7.65 4 6 9 16.82 0.72 12.43 5.4 6 10 16.71 2.08 6.09 2.7 6 11 14.2 5.28 7.79 4 Day - 1 is Monday, 2 is Tuesday….7 is Sunday Time - the hour the order came in (between 4 and 11pm) Assemble - time in minutes to assemble the order by Moe's cooks Wait - time in minutes from end of assembly to when Postmates delivery person arrived Deliver - time in minutes from pick up of order to when it arrives at customer's location Distance - miles between Moe's and customer's location

Explanation / Answer

a) What is the average total delivery time?

Answer:

The average total delivery time is given as 7.84 minutes approximately.

Deliver

Mean

7.841458333

Standard Error

0.122371028

Median

7.905

Mode

6.31

Standard Deviation

1.895763819

Sample Variance

3.593920459

Kurtosis

-0.23449713

Skewness

0.072401564

Range

9.46

Minimum

3.12

Maximum

12.58

Sum

1881.95

Count

240

b) The company’s goal is to have 95% of all orders delivered within 26 minutes. Conduct the appropriate statistical test to see if you think this is possible.

Here, we have to use one sample t test for the population. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: Average delivery time for orders is 26 minutes.

Alternative hypothesis: Ha: Average delivery time for orders is less than 26 minutes. (all orders delivered within 26 minutes.)

H0: µ = 26 versus Ha: µ < 26

This is a one tailed test. This is a lower tailed or left tailed test.

Test statistic formula is given as below:

Test statistic = t = (Xbar - µ) / [S/sqrt(n)]

We are given

Xbar = 7.84

S = 1.8958

n = 240

df = n – 1 = 240 – 1 = 239

c = 95% = 0.95

= 1 – c = 1 – 0.95 = 0.05

t = (7.84 – 26)/[1.8958/sqrt(240)]

t = -148.3983

P-value = 0.00 (by using t-table or excel)

P-value < = 0.05

So, we reject the null hypothesis that Average delivery time for orders is 26 minutes.

There is sufficient evidence to conclude that Average delivery time for orders is less than 26 minutes. (all orders delivered within 26 minutes.)

c) Does it take significantly more time for delivery on weekends than weekdays?

Here, we have to use two sample t test for the population mean.

Null hypothesis: H0: There is no significant difference in the average delivery time on weekdays and weekends.

Alternative hypothesis: Ha: There is a significant difference in the average delivery time on weekdays and weekends.

H0: µweekday = µweekend versus Ha: µweekday µweekend

This is a two tailed test.

We assume level of significance as = 0.05

For the given data, we have

Group Statistics

Day

N

Mean

Std. Deviation

Std. Error Mean

Delivery time in minutes

Weekends

72

7.8865

1.90978

.22507

Weekday

168

7.8221

1.89513

.14621

The test statistic formula is given as below:

t = (X1bar – X2bar) / sqrt[Sp2*((1/n1)+(1/n2))]

Where Sp2 is pooled variance

Sp2 = [(n1 – 1)*S1^2 + (n2 – 1)*S2^2]/(n1 + n2 – 2)

Sp2 = [(72 – 1)*1.90978^2 + (168 – 1)*1.89513^2]/(72 + 168 – 2)

Sp2 = 3.6081

SE = sqrt[Sp2*((1/n1)+(1/n2))]

SE = sqrt[3.6081*((1/72)+(1/168))]

SE = 0.2676

(X1bar – X2bar) = 7.8865 - 7.8221 = 0.0644

t = (X1bar – X2bar) / sqrt[Sp2*((1/n1)+(1/n2))]

t = 0.0644/0.2676

t = 0.24066

Lower critical value = -1.97

Upper critical value = 1.97

P-value = 0.81

= 0.05

P-value > = 0.05

So, we do not reject the null hypothesis that there is no significant difference in the average delivery time on weekdays and weekends.

There is sufficient evidence to conclude that the average delivery time on weekdays and weekends are same.

Deliver

Mean

7.841458333

Standard Error

0.122371028

Median

7.905

Mode

6.31

Standard Deviation

1.895763819

Sample Variance

3.593920459

Kurtosis

-0.23449713

Skewness

0.072401564

Range

9.46

Minimum

3.12

Maximum

12.58

Sum

1881.95

Count

240

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