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F statistic

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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

Sales person 1 56 208.8 2578.0
Sales person 2 65 191.0 2232.0
Sales person 3 144 213.4 2245.3
Sales person 4 147 201.2 2498.8

For these samples F= 3.71

Give the p- value corresponding to this value of the F statistic. Round answer to at least 3 decimal places.

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?

https://brainmass.com/statistics/f-test/f-statistic-136342

Solution Preview

To find the p-value, we have to look at an F-distribution table. But first, we have to figure out what degrees of freedom to use.

The degrees of freedom for the F statistic is made up of ...

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Sufficiency and Order Statistics

Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the uniform distribution over the closed interval [-theta, theta ]
having pdf f(x; theta ) = (1/2(theta))I[-theta , theta ](x).

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Define at least two ancillary statistics for this distribution

See attachment for better symbol representation.

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