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
Degrees of
Sum of
Mean square F statistic
variation
freedom
squares
Treatments
3806.74
(between
groups)
4
15,226.95
Error
(within
groups)
448
1,077,138.6
2404.33
Total
452
1,092,365.55
(b) How many total daily sales figures (the figures from all days for all salespeople) were used in the ANOVA?
(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) Using the 0.05 level of significance, what is the critical value of the F statistic for the ANOVA test? Round your answer to at least two 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?

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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