Question

An insurance company wants to know what whether perceptions of personal health are independent of gender. The company has hired you as a statistical consultant. You then collected a random sample of people and asked about their perceived health status. Based on the results of this survey, is the sex of the respondent independent from their perceived health status? Use 95% confidence.

Answer 1

The hypothesis being tested is:

H0: Sex of the respondent and perceived health status are independent

Ha: Sex of the respondent and perceived health status are not independent

		Women	Men	Total
Very Good	Observed	89	121	210
	Expected	104.27	105.73	210.00
	O - E	-15.27	15.27	0.00
	(O - E)² / E	2.24	2.20	4.44
Good	Observed	82	65	147
	Expected	72.99	74.01	147.00
	O - E	9.01	-9.01	0.00
	(O - E)² / E	1.11	1.10	2.21
Not so good	Observed	42	30	72
	Expected	35.75	36.25	72.00
	O - E	6.25	-6.25	0.00
	(O - E)² / E	1.09	1.08	2.17
Total	Observed	213	216	429
	Expected	213.00	216.00	429.00
	O - E	0.00	0.00	0.00
	(O - E)² / E	4.44	4.38	8.82
		8.82	chi-square
		2	df
		.0121	p-value

The p-value is 0.0121.

Since the p-value (0.0121) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that sex of the respondent and perceived health status are not independent.