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Maria Washington 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, Maria provides incentives for the four salespeople operating the food carts. This year, she plans to offer monetary bonuses to her salespeople based on their individual mean daily sales. Below is a chart giving a summary of the information that Maria has to work with. (In the chart, a "sample" is a collection of daily sales figures, in dollars, from this past year for a particular salesperson.) Groups Sample Sample Sample size mean variance Salesperson 1 88 209.8 2360.3 Salesperson 2 82 191.8 2049.0 Salesperson 3 123 215.8 2532.7 Salesperson 4 68 201.7 1527.0 Send data to calculator Send data to Excel Maria's first step is to decide if there are any significant differences in the mean daily sales of her salespeople. (If there are no significant differences, she'll split the bonus equally among the four of them.) To make this decision, Maria will do a one-way, independent-samples ANOVA test of equality of the population means, which uses the following statistic. Variation between the samples Variation within the samples For these samples, F =4.81. F= (a) Give the numerator degrees of freedom of this F statistic. 0 (b) Give the denominator degrees of freedom of this F 0 statistic. (c) Can we conclude, using the 0.05 level of significance, that at least one of the salespeople's mean daily sales is significantly different from that of the others? O Yes O No X

Maria Washington 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, Maria provides incentives for the four salespeople operating the food carts. This year, she plans to offer monetary bonuses to her salespeople based on their individual mean daily sales. Below is a chart giving a summary of the information that Maria has to work with. (In the chart, a "sample" is a collection of daily sales figures, in dollars, from this past year for a particular salesperson.) Groups Sample Sample Sample size mean variance Salesperson 1 88 209.8 2360.3 Salesperson 2 82 191.8 2049.0 Salesperson 3 123 215.8 2532.7 Salesperson 4 68 201.7 1527.0 Send data to calculator Send data to Excel Maria's first step is to decide if there are any significant differences in the mean daily sales of her salespeople. (If there are no significant differences, she'll split the bonus equally among the four of them.) To make this decision, Maria will do a one-way, independent-samples ANOVA test of equality of the population means, which uses the following statistic. Variation between the samples Variation within the samples For these samples, F =4.81. F= (a) Give the numerator degrees of freedom of this F statistic. 0 (b) Give the denominator degrees of freedom of this F 0 statistic. (c) Can we conclude, using the 0.05 level of significance, that at least one of the salespeople's mean daily sales is significantly different from that of the others? O Yes O No X

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 Washington 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, Maria provides incentives for the four salespeople operating the food carts. This year, she plans to offer monetary bonuses to her salespeople based on their individual mean daily sales. Below is a chart giving a summary of the information that Maria has to work with. (In the chart, a "sample" is a collection of daily sales figures, in dollars, from this past year for a particular salesperson.) Groups Sample Sample Sample size mean variance Salesperson 1 88 209.8 2360.3 Salesperson 2 82 191.8 2049.0 215.8 2532.7 Salesperson 3 123 Salesperson 4 68 201.7 1527.0 Send data to calculator V Send data to Excel Maria's first step is to decide if there are any significant differences in the mean daily sales of her salespeople. (If there are no significant differences, she'll split the bonus equally among the four of them.) To make this decision, Maria will do a one-way, independent-samples ANOVA test of equality of the population means, which uses the following statistic. Variation between the samples Variation within the samples For these samples, F≈4.81. F= (a) Give the numerator degrees of freedom of this F 10 statistic. (b) Give the denominator degrees of freedom of this F statistic. (c) Can we conclude, using the 0.05 level of significance, that at least one of the salespeople's mean daily sales is significantly different from that of the others? O Yes O No x
Transcribed Image Text:Maria Washington 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, Maria provides incentives for the four salespeople operating the food carts. This year, she plans to offer monetary bonuses to her salespeople based on their individual mean daily sales. Below is a chart giving a summary of the information that Maria has to work with. (In the chart, a "sample" is a collection of daily sales figures, in dollars, from this past year for a particular salesperson.) Groups Sample Sample Sample size mean variance Salesperson 1 88 209.8 2360.3 Salesperson 2 82 191.8 2049.0 215.8 2532.7 Salesperson 3 123 Salesperson 4 68 201.7 1527.0 Send data to calculator V Send data to Excel Maria's first step is to decide if there are any significant differences in the mean daily sales of her salespeople. (If there are no significant differences, she'll split the bonus equally among the four of them.) To make this decision, Maria will do a one-way, independent-samples ANOVA test of equality of the population means, which uses the following statistic. Variation between the samples Variation within the samples For these samples, F≈4.81. F= (a) Give the numerator degrees of freedom of this F 10 statistic. (b) Give the denominator degrees of freedom of this F statistic. (c) Can we conclude, using the 0.05 level of significance, that at least one of the salespeople's mean daily sales is significantly different from that of the others? O Yes O No x
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