Question

The table below shows the age and favourite type of music of 668 randomly selected people.

	Rock	Pop	Classical
15-25	50	85	73
25-35	68	91	60
35-45	90	74	77

Use a 5 percent level of significance to test the null hypothesis that age and preferred music type are independent.

(a) State the null and alternative hypotheses for this test. [2 marks]

(b) Calculate:

1. the expected frequency, E21, for age 25-35 years and favourite music is Rock

(ii) the chi-square contribution, X², for age 25-35 years and favourite music is Rock

Given that the chi-square test statistic, X² is 12.954, find the p-value for test [3 marks]

(c) State the conclusion for the test. [3 marks]

(d) State 2 limitations of the chi-square test X². [2 marks]

Answer 1

a)

null hypothesis: Ho: age and preferred music type are independent

alternate hypothesis:Ha: age and preferred music type are dependent

b)

expected frequency =rw total *column total/grand total =219*208/668=68.192

ii) chi-square contribution=0.0005~ 0.001

p-value for test =0.0115

c)as p value is less than 0.05 level of significance ; we reject the null hypothesis

we have sufficient evidence to conclude that age and preferred music type are dependent

d)

it is sensitve to sample size

expected frequency in each cell must be at least 5.