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, Cris 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 Cris 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

Salesperson 1 146 212.6 2003.5

Salesperson 2 88 205.3 2749.3

Salesperson 3 55 193.3 1658.2

Salesperson 4 86 215.6 2650.9

Cris' 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, Cris 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=3.21

Give the numerator degrees of freedom of this F statistic:

Give the denominator degrees of freedom of this F statistic:

Can we conclude, using the 0.10 level of significance, that at least one of the salepeople's mean daily sales is significantly different from that of others? yes or no