Question

•Example: A manager of a liquor store believes that the proportions of customers preferring CURES Beer, HAMMERKILL Beer, and MULER Beer are 40%, 30% and 30% respectively. The following results were obtained from a random sample of 200 customers:

	Cures	Hammerkill	Muler
#choosing this brand	70	63	67

•a) What type of data do we have here?

•b) Do the data provide sufficient evidence to indicate that the distribution of customer preferences is significantly different from the manager’s belief? Use a 1% level of significance.

Answer 1

a)

Type of data : Nominal ; Discrete;

b)

Null hypothesis : H_o : distribution of customer preferences is same as that from the manager’s belief

i.e ; Distribution of CURES Beer, HAMMERKILL Beer, and MULER Beer are 40%, 30% and 30%

Alternate hypothesis : H_a : distribution of customer preferences is not same as that from the manager’s belief

Test Statistic

Observed Frequency :O

	Observed frequency
CURES Beer	70
HAMMERKILL Beer	63
MULER Beer	67

Sample size : 200

Expected Frequency :E

For

CURES Beer : 40% of 200=80

HAMMERKILL Beer : 30% of 200 = 60

MULER Beer : 30% of 200 = 60

Degrees of freedom = number of types of beer - 1 = 3-1=2

p-value :

for 2 degrees of freedom,

Level of significance : : 0.01

As P-value : 0.3301 > Level of significance : : 0.01 fail to reject null hypothesis;

The data does not provide sufficient evidence to indicate that the distribution of customer preferences is significantly different from the manager’s belief