The owner of a chain of mini-markets wants to compare the sales performance of two of her stores, Store 1 and Store 2. Though the two stores have been comparable in the past, the owner has made several improvements to Store 1 and wishes to see if the improvements have made Store 1 more popular than 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 10 days, chosen at random. 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 Store 1 478 478 770 795 952 774 499 953 695 964 Store 2 329 581 595 921 895 661 645 793 575 973 Difference(Store 1 - Store 2) 149 −103 175 −126 57 113 −146 160 120 −9 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 Store 1 exceeds that of Store 2? 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 one-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:=μd0 H1:>μd0 (b) Determine the type of test statistic to use. Type of test statistic: ▼t Degrees of freedom: 9 (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the critical value at the 0.05 level of significance. (Round to three or more decimal places.) (e) At the 0.05 level, can the owner conclude that the mean daily sales of Store 1 exceeds that of Store 2?

The owner of a chain of mini-markets wants to compare the sales performance of two of her stores, Store 1 and Store 2. Though the two stores have been comparable in the past, the owner has made several improvements to Store 1 and wishes to see if the improvements have made Store 1 more popular than 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 10 days, chosen at random. 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 Store 1 478 478 770 795 952 774 499 953 695 964 Store 2 329 581 595 921 895 661 645 793 575 973 Difference(Store 1 - Store 2) 149 −103 175 −126 57 113 −146 160 120 −9 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 Store 1 exceeds that of Store 2? 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 one-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:=μd0 H1:>μd0 (b) Determine the type of test statistic to use. Type of test statistic: ▼t Degrees of freedom: 9 (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the critical value at the 0.05 level of significance. (Round to three or more decimal places.) (e) At the 0.05 level, can the owner conclude that the mean daily sales of Store 1 exceeds that of Store 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

See similar textbooks

Related questions

Question

100%

days, chosen at random. 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
Store 1	478	478	770	795	952	774	499	953	695	964
Store 2	329	581	595	921	895	661	645	793	575	973
Difference (Store 1 - Store 2)	149	−103	175	−126	57	113	−146	160	120	−9

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 Store 1 exceeds that of Store 2? 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 one-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:=μd0
H1:>μd0
(b)	Determine the type of test statistic to use.
	Type of test statistic: ▼t	Degrees of freedom: 9
(c)	Find the value of the test statistic. (Round to three or more decimal places.)

(d)	Find the critical value at the 0.05 level of significance. (Round to three or more decimal places.)

(e)	At the 0.05 level, can the owner conclude that the mean daily sales of Store 1 exceeds that of Store 2?

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 + ...

AI-Generated Solution

AI-generated content may present inaccurate or offensive content that does not represent bartleby’s views.

Unlock instant AI solutions

Tap the button
to generate a solution

Click the button to generate
a solution

SEE SOLUTION