The table below shows the earnings, in thousands of dollars, for three different commissioned employees. $2,000 + 3% on all sale
s 7% on all sales 5% on the first $40,000 + 8% on anything over $40,000 December 4.4 5.6 5.2 January 3.5 3.85 3.6 February 4.7 4.9 4.4 Who had the largest dollar amount in sales for the month of January? a. The salary plus commission employee.
b. The straight commission employee.
c. The graduated commission employee. d. They each had the same dollar amount in sales.
The salary plus commission employee earned $3,500 in January. Let his amount of sales for the month of January be x, then $2,000 + 3% of x = $3,500.
0.03x = $3,500 - $2,000 = $1,500
x = $1,500 / 0.03 = $50,000
The straight commission employee earned $3,850 in January. Let his amount of sales for the month of January be y, then 7% of y = $3,850.
0.07y = $3,850
y = $3,850 / 0.07 = $55,000
The graduated commission employee earned $3,600 in January. Let his amount of sales for the month of January be z, then 5% of $40,000 + 8% of z = $3,600.
0.05 x 40,000 + 0.08z = $3,600
$2,000 + 0.08z = $3,600
0.08z = $3,600 - $2,000 = $1,600
z = $1,600 / 0.08 = $20,000
Total sales for the graduated commission employee<span> = $40,000 + $20,000 = $60,000
Therefore, the graduated commission employee had the largest dollar amount in sales of $60,000 for the month of January</span>
F test is a statistical method used to determine which models best fits the population from which the sample is derived. It is a ratio of two variances. Variance measure the rate of dispersion
The formula for calculating f-test = explained variance / unexplained variance
There are two hypothesis in an f test :
1. the null hypothesis - all slope coefficient are equal to zero
the alternative hypothesis : at least one of the slope coefficient is not equal to zero
