A. Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.)B. At the 0.05 level, can the owner conclude that the mean daily sales of the two stores differ? 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 considerablydepending 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 thesame 12 days, chosen at random. She records the sales (in dollars) for each store on these days, as shown in the table below.DayStore 1Store 21843Difference(Store 1 - Store 2)Send data to calculator v2627 7072167948737656074838923158 - 855729 2445636166417- 173789557 381 791628 258 602105224771191312700757 825-71 123 189 45 156 - 125Based on these data, can the owner conclude, at the 0.05 level of significance, that the mean daily sales of the two stores differ? Answer this question byperforming a hypothesis test regarding μ (which is u with a letter "d" subscript), the population mean daily sales difference between the two stores. Assumethat this population of differences (Store 1 minus Store 2) is normally distributed.Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers asspecified. (If necessary, consult a list of formulas.)Español?

Given: Sample size n = 12 Significance level α = 0.05 Formula Used: Test-statistic t = d-μdsdn

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 12 days, chosen at random. She records the sales (in dollars) for each store on these days, as shown in the table below. 89 10 11 12 Day Store 1 Store 2 1 2 Difference (Store 1 - Store 2) Send data to calculator V 3 216 843 794 765 838 729 4 5 87 158 6 627 707 607 923 563 417 628 258 602 477 757 825 -85 166 7 244 557 381 791 522 913 700 -173 -71 123 189 45 156 -125 Based on these data, can the owner conclude, at the 0.05 level of significance, that the mean daily sales of the two stores differ? Answer this question by performing a hypothesis test regarding (which is u 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. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified (If necessary consult a list of formulas ) Español

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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Question

A. Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.)

B. At the 0.05 level, can the owner conclude that the mean daily sales of the two stores differ?

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 12 days, chosen at random. She records the sales (in dollars) for each store on these days, as shown in the table below.
Day
Store 1
Store 2
1
843
Difference
(Store 1 - Store 2)
Send data to calculator v
2
627 707
216
794
87
3
765
607
4
838
923
158 - 85
5
729 244
563
6
166
417
- 173
7
8
9
557 381 791
628 258 602
10
522
477
11
913
12
700
757 825
-71 123 189 45 156 - 125
Based on these data, can the owner conclude, at the 0.05 level of significance, that the mean daily sales of the two stores differ? Answer this question by
performing a hypothesis test regarding μ (which is u 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. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as
specified. (If necessary, consult a list of formulas.)
Español
?

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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