Question

Perform a chi-squared hypothesis test on the following table. (Hint: You can use the website demonstrate in the lecture to calculate the chi-squared test statistic). Show all 4 steps.

Association between nurse work fatigue and flu.

	Developed flu	Did not develop flu	Total
Worked > 40 hours/week	38	148	186
Worked ≤ 40 hours/week	13	156	169
Total	51	304	355

Ethnic Group	Laid Off	Not Laid Off	Total
Black Americans	130	1382	1512
White Americans	87	2813	2900
Total	217	4195	4412

Using the contingency table above, calculate the odds of being laid off for white Americans. Leave your answer as a proportion and round to 2 decimal places.

Answer 1

The hypothesis being tested is:

H₀: There is no association between nurse work fatigue and flu

H_a: There is an association between nurse work fatigue and flu

		Col 1	Col 2	Total
Row 1	Observed	38	148	186
	Expected	26.72	159.28	186.00
	O - E	11.28	-11.28	0.00
	(O - E)² / E	4.76	0.80	5.56
Row 2	Observed	13	156	169
	Expected	24.28	144.72	169.00
	O - E	-11.28	11.28	0.00
	(O - E)² / E	5.24	0.88	6.12
Total	Observed	51	304	355
	Expected	51.00	304.00	355.00
	O - E	0.00	0.00	0.00
	(O - E)² / E	10.00	1.68	11.68
		11.68	chi-square
		1	df
		.0006	p-value

The chi-square test statistic is 11.68.

The p-value is 0.0006

Since the p-value (0.0006) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is an association between nurse work fatigue and flu.

The odds of being laid off for white Americans = 2813/87 = 32.33 to 1