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 12 days, she records the sales (in dollars) for each store on these days, as shown in the table below. Day 1 2 3 4 5 6 7 8 9 10 11 12 Store 1 504 909 591 658 232 697 236 425 659 625 737 772 Store 2 298 845 660 635 31 572 400 455 745 554 518 753 Difference (Store 1 - Store 2) 206 64 −69 23 201 125 −164 −30 −86 71 219 19 Send data to calculator 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 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. 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.) (a) State the null hypothesis H0 and the alternative hypothesis H1 . H0: H1: (b) Determine the type of test statistic to use. Type of test statistic: ▼(Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.) and (e) At the 0.05 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 the table below.

Day	1	2	3	4	5	6	7	8	9	10	11	12
Store 1	504	909	591	658	232	697	236	425	659	625	737	772
Store 2	298	845	660	635	31	572	400	455	745	554	518	753
Difference (Store 1 - Store 2)	206	64	−69	23	201	125	−164	−30	−86	71	219	19

Send data to calculator

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

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. 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.)

(a)	State the null hypothesis H0 and the alternative hypothesis H1 .
H0:
H1:
(b)	Determine the type of test statistic to use.
	Type of test statistic: ▼(Choose one)
(c)	Find the value of the test statistic. (Round to three or more decimal places.)

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