Question

In the book Business Research Methods (5th ed.), Donald R. Cooper and C. William Emory discuss studying the relationship between on-the-job accidents and smoking. Cooper and Emory describe the study as follows:

Suppose a manager implementing a smoke-free workplace policy is interested in whether smoking affects worker accidents. Since the company has complete reports of on-the-job accidents, she draws a sample of names of workers who were involved in accidents during the last year. A similar sample from among workers who had no reported accidents in the last year is drawn. She interviews members of both groups to determine if they are smokers or not.

The sample results are given in the following table.

	On-the-Job Accident
Smoker	Yes		No		Row Total
Heavy	12		8		20
Moderate	9		10		19
Nonsmoker	13		14		27
Column total	34		32		66

Expected counts are below observed counts
	Accident		No Accident		Total
Heavy	12		8		20
	10.30		9.70
Moderate	9		10		19
	9.79		9.21
Nonsmoker	13		14		27
	13.91		13.09
Total	34		32		66
Chi-Sq = .83, DF = 2, P-Value = 0.660

(a) For each row and column total in the above table, find the corresponding row/column percentage. (Round your answers to 2 decimal places.)

Row 1	%
Row 2	%
Row 3	%
Column 1	%
Column 2	%

(b) For each cell in the above table, find the corresponding cell, row, and column percentages. (Round your answers to 2 decimal places.)

	Accident	No Accident
Heavy	Cell=  %	Cell=  %
	Row=  %	Row=  %
	Column=  %	Column=  %
Moderate	Cell=  %	Cell=  %
	Row=  %	Row=  %
	Column=  %	Column=  %
Nonsmoker	Cell=  %	Cell=  %
	Row=  %	Row=  %
	Column=  %	Column=  %

(c) Use the MINITAB output in the above to test the hypothesis that the incidence of on-the-job accidents is independent of smoking habits. Set α = .01.

(Click to select)Do not rejectReject H₀.

(d) Is there a difference in on-the-job accident occurrences between smokers and nonsmokers?

Conclude there is (Click to select)no differencedifference between smokers and nonsmokers.

Answer 1

Solution:-

A)

	Percentage
Row 1	30.30%
Row 2	28.79%
Row 3	40.91%
Column 1	51.52%
Column 2	48.48%

b)

	Accident	No Accident
Heavy	Cell = 18.18%	Cell = 12.12%
	Row = 60 %	Row = 40%
	Column = 35.29 %	Column = 25%
Moderate	Cell = 13.64%	Cell = 15.15%
	Row = 47.37%	Row = 52.63%
	Column = 26.47%	Column = 31.25 %
Nonsmoker	Cell = 19.70%	Cell = 21.21%
	Row = 48.15%	Row = 51.85%
	Column = 38.24 %	Column = 43.75 %

c)

Smoker	Yes	Expected	[(Or,c - Er,c)2/ Er,c]	No	Expected	[(Or,c - Er,c)2/ Er,c]	Total
Heavy	12	10	0.279500891	8	9.696969697	0.296969697	20
Moderate	9	10	0.063420584	10	9.212121212	0.06738437	19
Nonsmoker	13	14	0.059417706	14	13.09090909	0.063131313	27
Total	34	34	0.40	32.00	32.00	0.43	66

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

H₀: Incidence of on-the-job accidents is independent of smoking habits
H_a: Incidence of on-the-job accidents is not independent of smoking habits.

Formulate an analysis plan. For this analysis, the significance level is 0.01. Using sample data, we will conduct a chi-square test for independence.

Analyze sample data. Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

1) The sampling method is simple random sampling.

2) The variables under study are each categorical.

3) If sample data are displayed in a contingency table, the expected frequency count for each cell of the table is at least 5.

DF = (r - 1) * (c - 1) = (2 - 1) * (3 - 1)
D.F = 2
E_r,c = (n_r * n_c) / n

Χ² = 0.83

where DF is the degrees of freedom.

The P-value is the probability that a chi-square statistic having 2 degrees of freedom is more extreme than 0.82.

We use the Chi-Square Distribution Calculator to find P(Χ² > 0.83) = 0.66

Interpret results. Since the P-value (0.66) is greater than the significance level (0.01), we have to accept the null hypothesis.

Thus, we conclude that the incidence of on-the-job accidents is independent of smoking habits.

d) No, there is no difference in on-the-job accident occurrences between smokers and nonsmokers.