Diane Alexander 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, Diane 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 Diane's ANOVA. 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 Between 19,710.92 3942.18 groups Error 754 2,130,826.3 2826.03 (within groups) Total 759 2,150,537.22

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Question #7

Diane Alexander 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, Diane 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 Diane's 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
Between
5
19,710.92
3942.18
groups
Error
754
2,130,826.3
2826.03
(within
groups)
Total
759
2,150,537.22
Transcribed Image Text:Diane Alexander 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, Diane 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 Diane's 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 Between 5 19,710.92 3942.18 groups Error 754 2,130,826.3 2826.03 (within groups) Total 759 2,150,537.22
(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 0.01 level of significance, that at least one salesperson's mean daily sales is significantly different from that of the others?
OYes
ONo
?
Transcribed Image Text:(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 0.01 level of significance, that at least one salesperson's mean daily sales is significantly different from that of the others? OYes ONo ?
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