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 the table below. Day 1 2 3 4 5 6 7 8 9 10 Store 1 293 696 466 336 444 682 949 278 697 817 Store 2 127 739 220 441 303 471 680 119 791 585 Difference (Store 1 - Store 2) 166 −43 246 −105 141 211 269 159 −94 232 Based on these data, can the owner conclude, at the 0.01 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. a. State the null hypothesis H0 and the alternative hypothesis H1. b. Find the value of the test statistic. Round to three or more decimal places. c. Find the two critical values at the 0.01 level of significance. Round to three or more decimal places. d. At the 0.01 level, can the owner conclude that the mean daily sales of the two stores differ?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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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 10 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
Store 1	293	696	466	336	444	682	949	278	697	817
Store 2	127	739	220	441	303	471	680	119	791	585
Difference (Store 1 - Store 2)	166	−43	246	−105	141	211	269	159	−94	232

Based on these data, can the owner conclude, at the 0.01 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.

a. State the null hypothesis H0 and the alternative hypothesis H1.

b. Find the value of the test statistic. Round to three or more decimal places.

c. Find the two critical values at the 0.01 level of significance. Round to three or more decimal places.

d. At the 0.01 level, can the owner conclude that the mean daily sales of the two stores differ?

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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