Problem

A mobile phone company offers an insurance policy to its customers when they purchase a mobile phone. The company conducted a survey on the age of the customers and whether or not claims were made.

A random sample of 1200 customers from this company was investigated for 2020 and the results are shown in the table below.

Age	Claim made in 2020	No claim made in 2020	Total
17 – 20 years	24	176	200
21 – 50 years	48	652	700
51 years and over	14	286	300
Total	86	1114	1200

The data are to be used to determine whether or not making a claim is independent of age.

(a) Calculate the expected frequencies for the age group 51 years and over that (i) made a claim in 2020 (ii) did not make a claim in 2020

The 4 classes of customers aged between 17 and 50 give a value of

$$\sum \frac{(O-E)^2}{E}=7.123$$

correct to 3 decimal places.

(b) Test, at the 1% level of significance, whether or not making a claim is independent of age. Show your working clearly, stating your hypotheses, the degrees of freedom, the test statistic and the critical value used.