Chris 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, Chris 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 Chris 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 size Sample mean Sample Variance
Sales person 1 55 222.0 3302.5
Sales person 2 59 199.7 2370.4
Sales person 3 89 219.3 2813.0
Sales person 4 125 202.9 2254.7
Chris' 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, Chris will do a one-way, independent-samples ANOVA test of equality of the population means, which uses the statistic
F= Variation between the samples/variation within the samples
For these samples, F = 3.65
1. Give the numerator degree of freedom of this F statistic?
2. Give the denominator of degree of freedom of this F statistic?
3. Can we conclude, using the 0.10 level of significance, that at least one of the sales people's mean daily sales is significantly different from that of others? Yes or no
(Please see attached file)
A Complete, Neat and Step-by-step Solution is provided in the attached file.