Answered: Cris Turlock owns and manages a small…

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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Cris Turlock owns and manages a small business in San Francisco, California. The business provides breakfast and brunch food, via carts parked along sidewalks, to people in the business district of the city.

Being an experienced businessperson, Cris provides incentives for the salespeople operating the food carts. This year, she plans to offer monetary bonuses to her salespeople based on their individual mean daily sales. Her first task is to see if there is a significant difference in the mean daily sales among the different salespeople. She chooses a "sample" of days for each salesperson and records the sales for each day. She then runs a one-way, independent-samples ANOVA test to determine whether or not she can conclude that at least one salesperson's performances is significantly different from the others. (Otherwise, she'll split the bonuses evenly among all the salespeople.) In her ANOVA, the "groups" are the different salespeople, and the variable of interest is the daily sales amount, in dollars.

(a)Below is an ANOVA table summarizing Cris' ANOVA. Fill in the missing cell of the table (round your answer to at least two decimal places).

Source of variation	Degrees of freedom	Sum of squares	Mean square
Treatments (between groups)	5	33,956.29	6791.26
Error (within groups)	598	1,596,027.1	2668.94
Total	603	1,629,983.39

(b)How many salespeople were included in the analysis?

(c)For the ANOVA test, it is assumed that the population variance of daily sales is the same for each salesperson. What is an unbiased estimate of this common population variance based on the sample variances?

(d)What is the p-value corresponding to the F statistic for the ANOVA test? Round your answer to at least three decimal places.

(e)Can we conclude, using the

0.05

level of significance, that at least one salesperson's mean daily sales is significantly different from that of the others?

Yes

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