Problem

A local village radio station, LSB, decides to survey adults in its broadcasting area about the programmes it produces.

LSB broadcasts to 4 villages A, B, C and D. The number of households in each of the villages is given below.

Village	Number of households
A	41
B	164
C	123
D	82

LSB decides to take a stratified sample of 200 households.

(a) Explain how to select the households for this stratified sample.

One of the questions in the survey related to the age group of each member of the household and whether they listen to LSB. The data received are shown below.

Age group	18–49	50–69	Older than 69
Listen to LSB	130	162	65
Do not listen to LSB	78	98	62

The data are to be used to determine whether or not there is an association between the age group and whether they listen to LSB.

(b) Calculate the expected frequencies for the age group 50–69 that

(i) listen to LSB

(ii) do not listen to LSB

Given that for the other 4 classes $\sum \dfrac{(O-E)^2}{E} = 4.657$ to 3 decimal places,

(c) test at the 5% level of significance whether or not there is evidence of an association between age and listening to LSB. Show your working clearly, stating the degrees of freedom and the critical value.