The owner of a chain of mini-markets wants to compare the sales performance of two of her stores, Store 1 and Store 2. Sales can vary considerably depending on the day of the week and the season of the year, so she decides to eliminate such effects by making sure to record each store's sales on the same sample of days. After choosing a random sample of 10 days, she records the sales (in dollars) for each store on these days, as shown in Table 1. Day Store 1 Store 2 Difference(Store 1 - Store 2) 1 927 759 168 2 327 312 15 3 872 645 227 4 330 332 -2 5 684 711 -27 6 625 471 154 7 436 557 -121 8 615 694 -79 9 674 632 42 10 975 1013 -38 Table 1 Based on these data, can the owner conclude, at the 0.10 level of significance, that the mean daily sales of the two stores differ? Answer this question by performing a hypothesis test regarding μd (which is μ with a letter "d" subscript), the population mean daily sales difference between the two stores. Assume that this population of differences (Store 1 minus Store 2) is normally distributed. Perform a two-tailed test. The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic:(Round to at least three decimal places.) The two critical values at the 0.10 level of significance:(Round to at least three decimal places.) and At the 0.10 level, can the owner conclude that the mean daily sales of the two stores differ? Yes No

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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The owner of a chain of mini-markets wants to compare the sales performance of two of her stores, Store 1 and Store 2. Sales can vary considerably depending on the day of the week and the season of the year, so she decides to eliminate such effects by making sure to record each store's sales on the same sample of days. After choosing a random sample of

days, she records the sales (in dollars) for each store on these days, as shown in Table 1.

Day	Store 1	Store 2	Difference (Store 1 - Store 2)
1	927	759	168
2	327	312	15
3	872	645	227
4	330	332	-2
5	684	711	-27
6	625	471	154
7	436	557	-121
8	615	694	-79
9	674	632	42
10	975	1013	-38

Table 1

Based on these data, can the owner conclude, at the

0.10

level of significance, that the mean daily sales of the two stores differ? Answer this question by performing a hypothesis test regarding

μd

(which is

with a letter "d" subscript), the population mean daily sales difference between the two stores. Assume that this population of differences (Store 1 minus Store 2) is normally distributed.

Perform a two-tailed test.


The null hypothesis:	H0:
The alternative hypothesis:	H1:
The type of test statistic:	(Choose one)ZtChi squareF

The value of the test statistic: (Round to at least three decimal places.)
The two critical values at the 0.10 level of significance: (Round to at least three decimal places.)	and
At the 0.10 level, can the owner conclude that the mean daily sales of the two stores differ?	Yes	No

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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