ANOVA Test and F-Statistic
Please see attached file for full problem description.
Cris 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
Salesper 1 128 207.4 2810.0
Sales per2 115 213.4 2519.2
Sale per 3 81 193.8 2667.6
Sale pers4 112 215.4 2144.0
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
Variation between the samples .
Variation within the samples
For these samples, .
Give the p value corresponding to this value of the F statistic. Round yoru answer to at leas three decimal places.
Can we conclude using the 0.05 level of significance, that at least one of the salespersons mean daily sales is significantly different from that of the others