Question

The ABC Logistics Company wishes to test a new truck routing algorithm. A random sample of 20 trucks are enrolled in the test. The trucks are randomly assigned to two groups. Trucks in the first group are routed using the current algorithm. Trucks in the second group are routed using the proposed new algorithm. Performance of the algorithm is measured by the number of packages delivered on the test day.

Routing Algorithms	Number of Packages Delivered	Sample Mean	Sample Standard Deviation
Current Routing Algorithm	100, 106, 103, 105, 101, 103, 104, 101, 103, 102
Proposed New Routing Algorithm	108, 109, 103, 106, 108, 107, 104, 105, 106, 104

1. Use the P-value approach to test on whether the mean number of packages delivered are the same between the two groups. Assuming the variances are equal between the two groups.

2. Calculate the Cohen’s d.

Answer 1

Answer:-

Given That:-

The ABC Logistics Company wishes to test a new truck routing algorithm. A random sample of 20 trucks are enrolled in the test. The trucks are randomly assigned to two groups. Trucks in the first group are routed using the current algorithm. Trucks in the second group are routed using the proposed new algorithm. Performance of the algorithm is measured by the number of packages delivered on the test day.

Routing Algorithms	Number of Packages Delivered	Sample Mean	Sample Standard Deviation
Current Routing Algorithm	100,106,103,105,101,103,104,101,103,102
Proposed New Routing Algorithm	108,109,103,106,108,107,104,105,106,104

a.Use the P-value approach to test on whether the mean number of packages delivered are the same between the two groups. Assuming the variances are equal between the two groups.?

data -> data analysis ->

t-Test: Two-Sample Assuming Equal Variances

t-Test: Two-Sample Assuming Equal Variances
	Variable 1	Variable 2
Mean	102.8	106
Variance	3.5111111	4
Observations	10	10
Pooled Variance	3.7555556
Hypothesized Mean Difference	0
df	18
t Stat	-3.6923077
P(T<=t) one-tail	0 .0008335
t Critical one-tail	1.7340636
P(T<=t) two-tail	0.001667
t Critical two-tail	2.100922

p-value = 0.001667

since p-value < alpha

we reject the null hypothesis

we conclude that there is sufficient evidence that means are not equal
b.Calculate the Cohen’s d.?

cohen's d = |TS| * sqrt(1/n1 + 1/n2)

= 3.6923 * sqrt(1/10 + 1/10)

= 1.6512