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?

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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Related questions

Question

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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?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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