Paired Mean Difference TestingOnline shop "ABC" sends consumer goods using the "PT. Express shipments "for 2018 and contracted with Shipping Services" PT. Express Package ”for delivery in 2019. Management wants to know the average delivery time between the two delivery service companies. The results from a random sample of 12 sub-districts in 2018 and 2019 are presented in the following table.Sub-DistrictFast Submissions, 2018 Average Travel Time (minutes)Express Package, 2019 Average Travel Time (minutes)121026023203803300370435039054004006450500750060085506009600650107507501180085012750850Do Express Delivery Companies deliver goods faster than Express Parcel Companies? Test it using 5% negligence.What do you recommend "ABC" store management?

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Description: Paired Mean Difference TestingOnline shop "ABC" sends consumer goods using the "PT. Express shipments "for 2018 and contracted with Shipping Services" PT. Express Package ”for delivery in 2019. Management wants to know the average delivery time betwe

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Paired Mean Difference Testing

Online shop "ABC" sends consumer goods using the "PT. Express shipments "for 2018 and contracted with Shipping Services" PT. Express Package ”for delivery in 2019. Management wants to know the average delivery time between the two delivery service companies. The results from a random sample of 12 sub-districts in 2018 and 2019 are presented in the following table.

Sub-District	Fast Submissions, 2018 Average Travel Time (minutes)	Express Package, 2019 Average Travel Time (minutes)
1	210	260
2	320	380
3	300	370
4	350	390
5	400	400
6	450	500
7	500	600
8	550	600
9	600	650
10	750	750
11	800	850
12	750	850

Do Express Delivery Companies deliver goods faster than Express Parcel Companies? Test it using 5% negligence.
What do you recommend "ABC" store management?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Step 1 Set the null hypothesis

$T o t e s t H_{0} : μ_{d} = 0 H_{1} : μ_{d} \neq 0$

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