Question

11. A manager at a manufacturing plant gathers data to see whether or not the incidence of on-the-job accidents is related to workers’ smoking habits. A total of 66 employees are surveyed about their smoking habits and their accident records are examined. The MegaStat output below shows the observed absolute frequencies (in bold) along with the results of a χ²(Chi-square) test in a Contingency Table.

1. (3 pts.) Write out the Ho (in words) for a test for independence.

2. (4 pts.) Explain how the expected number of heavy smokers with accidents (8.24) is calculated.

3. (4 pts.) Interpret these results (for α = .01). Can we reject Ho? Explain.

Chi-square Contingency Table Test for Independence
			Accident	No Accident	Total
	Heavy	Observed	12	4	16
	Smoker	Expected	8.24	7.76	16.00
		% of row	75.0%	25.0%	100.0%
		% of column	35.3%	12.5%	24.2%
	Moderate	Observed	9	6	15
	Smoker	Expected	7.73	7.27	15.00
		% of row	60.0%	40.0%	100.0%
		% of column	26.5%	18.8%	22.7%
	Nonsmoker	Observed	13	22	35
		Expected	18.03	16.97	35.00
		% of row	37.1%	62.9%	100.0%
		% of column	38.2%	68.8%	53.0%
	Total	Observed	34	32	66
		Expected	34.00	32.00	66.00
		% of row	51.5%	48.5%	100.0%
		% of column	100.0%	100.0%	100.0%
			6.86	chi-square
			2	df
			.0324	p-value

Answer 1

Answer:

(a)

(b)

(c) Since the P-value = 0.0324 > 0.01, we fail to reject H0.

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