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Maria owns and manages a small business, selling food via carts to people in the business district of her city. She 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 Maria's ANOVA. Fill in the missing cell of the table. (Round your answer to at least two decimal places.) 8 Source of Degrees of variation freedom Sum of squares Mean square F statistic X Between groups Error (within groups) 5 47,952.14 9590.43 500 1,286,335.10 2572.67 Total 505 1,334,287.24 (b) How many total daily sales figures (the figures from all days for all salespeople) were used in the ANOVA? G (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? 0 G (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. 0 X 5 (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 No G

Maria owns and manages a small business, selling food via carts to people in the business district of her city. She 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 Maria's ANOVA. Fill in the missing cell of the table. (Round your answer to at least two decimal places.) 8 Source of Degrees of variation freedom Sum of squares Mean square F statistic X Between groups Error (within groups) 5 47,952.14 9590.43 500 1,286,335.10 2572.67 Total 505 1,334,287.24 (b) How many total daily sales figures (the figures from all days for all salespeople) were used in the ANOVA? G (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? 0 G (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. 0 X 5 (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 No G

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.2: Representing Data
Problem 22PFA
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Maria owns and manages a small business, selling food via carts to people in the business district of her city. She 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 Maria's ANOVA. Fill in the missing cell of the table. (Round your answer to at least two decimal places.) 8 Source of Degrees of variation freedom Sum of squares Mean square F statistic X Between groups Error (within groups) 5 47,952.14 9590.43 500 1,286,335.10 2572.67 Total 505 1,334,287.24 (b) How many total daily sales figures (the figures from all days for all salespeople) were used in the ANOVA? G (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? 0 G (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. 0 X 5 (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 No G
Transcribed Image Text:Maria owns and manages a small business, selling food via carts to people in the business district of her city. She 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 Maria's ANOVA. Fill in the missing cell of the table. (Round your answer to at least two decimal places.) 8 Source of Degrees of variation freedom Sum of squares Mean square F statistic X Between groups Error (within groups) 5 47,952.14 9590.43 500 1,286,335.10 2572.67 Total 505 1,334,287.24 (b) How many total daily sales figures (the figures from all days for all salespeople) were used in the ANOVA? G (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? 0 G (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. 0 X 5 (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 No G
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