statistic question

Question

According to an independent insurance agent, the following is a breakdown of the amount of life insurance purchased by males in the following age groups. The agent is interested in whether the age of the male and the amount of life insurance purchased are independent events. Conduct a test for independence at the 5% level.

20 – 29	45	15	45	0	5
30 – 39	35	5	25	20	5
40 – 49	15	0	30	0	30
50+	45	30	15	10	5

What is the test statistic? (Round your answer to two decimal places.)

Answer 1

1. Calculate Row Totals and Column Totals:

1. Calculate the Expected Counts:

Expected Count=(Row Total×Column Total)/Grand Total

For example, the expected count for the cell (20-29, $0-$49K) is:

Expected Count=110×140/380≈40.53

Age Group
20-29	40.53	14.47	33.29	8.68	13.03
30-39	33.16	11.84	27.24	7.11	10.66
40-49	27.63	9.87	22.71	5.93	8.89
50+	38.68	13.82	31.76	8.29	12.42

1. Calculate the Chi-Square Test Statistic:

The chi-square test statistic is calculated as:

𝜒2=∑(𝑂−𝐸)^2/E

Calculate for all cells and sum them up:

Age Group
20-29	0.50	0.02	4.48	8.68	5.14	18.82
30-39	0.11	3.95	0.18	25.42	2.99	32.65
40-49	5.48	9.87	3.53	5.93	49.45	74.26
50+	1.02	31.95	14.20	0.07	5.12	52.36

Summing all these values:

𝜒2≈178.09