Question

Market researchers have shown that background music can influence the purchasing behavior of customers. The owner of an independent bookstore wants to know if this is true for her bookstore. She recorded the amount customers spent when no music was playing, when classical music was playing and when jazz music was playing. She summarized the data as follows:

		Type of music
		None		Classical		Jazz		Total
Amount spent	Less than $50	22		20		18		60
	$50 or more	16		34		40		90
	Total	38		54		58		150

If a customer spent less than $50, what is the probability that there was classical music playing while they were in the bookstore? [2 marks]

ANSWER (4 decimal places):______________________

Among those customers who were in the store when music was playing, what percentage of them spent $50 or more? [2 marks]

ANSWER (Percentage, 2 decimal places):______________________

Is there enough evidence to conclude that the background music can influence the purchasing behavior of customers? Test at the 5% level of significance.   [8 marks]

H₀:                                                                                                                                         

H_A:                                                                                                                                         

Critical Value:                                                      Test Statistic:                                         

Decision:                                                                                                                   

Conclusion: Circle the Correct One:

Yes or no

Answer 1

a)P(Classical|<50)=20/60=1/3=0.3333

b)P(>50|Music)=(34+40)/(54+58)=0.6607

We need to conduct a Chi SQ test to check if there is an impact

H0:Background Music and purchasing behaviour are independent

Ha: Background Music and purchasing behaviour are not independent

For Expected table, as a sample, For classical and Less than 50->54*60/150=21.6. Similarly others.

Test Statistic=Sum(3.042+0.1185+1.165+2.028+0.079+0.777)=7.21

dof=(3-1)*(2-1)=2

Critical Chisq=5.99

Hence as Test stat>5.99, we reject H0 and say background music has an impact on purchasing behaviour