Answered: Similarity Test Average of 2…

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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Similarity Test Average of 2 populations

Delta Food Grocery has two grocery stores located in Bije City. One shop is located on Jalan Usman and the other on Jalan Sinda and each is run by a different manager. Every manager claims that his shop layout maximizes the number of impulsive customers. The two managers surveyed their sample of customers and asked them how much they were spending than they planned, in other words, how much they were spending on impulse (spending more than they planned). The following table shows sample data collected from the two shops.

Jalan Usman (in $ 000)	Jalan Sinda (in $ 000)
15.78	15.19
17.73	18.22
10.61	12.87
15.79	17.79
13.45	13.96
12.85	13.74
	12.47
	10.83
S₁=2.5529	S₂=2.5675

Top management at Delta Foods Grocery wanted to know if there was a difference in the mean amount of impulsive consumption between the two stores. Perform statistical analysis via:

Commpile the null hypothesis and alternative hypothesis
Help both managers test their hypothesis, Use alpha = 0.05
What is the conclusion?

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 + ...

Expert Solution

Step 1

$H_{0} : μ_{1} = μ_{2} (m e a n o f b o t h s t o r e s i s t h e s a m e) H_{1} : μ_{1} \neq μ_{2} (M e a n o f b o t h s t o r e s i s d i f f e r e n t)$

$μ_{1} = \frac{15.78 + 17.73 + 10.61 + 15.79 + 13.45 + 12.85}{6} = 14.368 μ_{2} = \frac{15.19 + 18.22 + 12.87 + 17.79 + 13.96 + 13.74 + 12.47 + 10.83}{8} = 14.383$

$n_{1} = 6 n_{2} = 8$

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