Question

Motivation Level	Talent
	High	Medium	Low	Total
High	6	18	6
Medium	21	35	6
Low	12	6	2
Total

Q1. Are high motivation and high talent independent? Justify your answer.

Adrian sells cars for Honest Joe’s car dealership. Adrian has never sold more than three cars in a given week. Given X is the number of cars sold by Adrian in a week, the probability distribution of X is summarized in the following table:

X	0	1	2	3
P(X)	p	0.45	0.25	0.05

(a) What is the probability of Adrian selling zero cars?

(b) What is the probability of Adrian selling at least two cars?

(c) What is the probability of Adrian selling no more than one car?

(d) Draw the probability distribution in a graphical form.

(e) Adrian gets paid a bonus of $500 if he sells one car per week. For each additional car sold per week Adrian receives $300. Calculate his mean bonus.

Answer 1

( 1 )

The following cross tablulation have been provided. The row and column total have been calculated and they are shown below:

Observed	Column 1	Column 2	Column 3	Total
Row 1	6	18	6	30
Row 2	21	35	6	62
Row 3	12	6	2	20
Total	39	59	14	112

Expected Values	Column 1	Column 2	Column 3	Total
Row 1	39*30/112 = 10.446	59*30/112 = 15.804	14*30/112 = 3.75	30
Row 2	39*62/112 = 21.589	59*62/112 = 32.661	14*62/112 = 7.75	62
Row 3	39*20/112 = 6.964	59*20/112 = 10.536	14*20/112 = 2.5	20
Total	39	59	14	112

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H0?: The high motivation and high talent are independent

Ha?: The high motivation and high talent

Assume alpha =0.05