Posted: April 11th, 2016

# Can we conclude using the 0.05 level of signifigance that at least one of the sales peoples mean daily sales is significantly different from that of others?

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 one 147 207.3 1944.2
Sales person two 127 218.8 2761.6
Sales person three 130 220.5 2449.4
Sales person four 111 218.9 2442.8
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= variance between the samples
variance within the samples
for these samples, f= 2.21
Give the p value correspondning to this value of the f statistic.Round to three decimal places.
Can we conclude using the 0.05 level of signifigance that at least one of the sales peoples mean daily sales is significantly different from that of others?

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