Question 195842: ANOVA: Degrees of freedom and the F statistic
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 Samples size Sample Mean Sample Variance
Salesperson 1 128 207.4 1868.4
Salesperson 2 149 207.6 2067.6
Salesperson 3 107 200.7 2594.9
Salesperson 4 51 193.6 2683.9
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=1.75
Give the p-value corresponding to this value of the F statistic. Round your ansewer to at least three decimal places? ____ hide problem
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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=1.75
Give the p-value corresponding to this value of the F statistic. Round your ansewer to at least three decimal places? ____ hide problem
Degrees of numerator freedom: c-1 = 4-1 = 3
Degrees of denominator freedom: n-c = 435-3 = 432
n = 128+149+107+51 = 435
F(3,432) = ?
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I don't have an F-chart that details the the area to the right of 1.75
for the degrees of freedom listed above.
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Cheers,
Stan H.
Salesperson 1 128 207.4 1868.4
Salesperson 2 149 207.6 2067.6
Salesperson 3 107 200.7 2594.9
Salesperson 4 51 193.6 2683.9
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