Question

2. Behavior of wearing seat belt has two categories: Most Times or Always and Rarely or Never. Overall Grades for Undergraduate Degree has three categories: A or B, C, and D or F. In a group of 1534 students with grades A or B, 1354 students wear seat belts Most time or Always. In a group of 553 students with grade C, 428 students wear seat belts Most Time or Always. In a group of 105 students with grades D or F, 65 wear seat belts Most Time or Always. Conduct a test the hypothesis at 5% level of significance that Wearing seat belts and Grades at Undergraduate degree are independent or not. Show all four steps.

Answer 1

SOLUTION:-

Step 1 : The null and alternative hypothesis

H0: Wearing Seat belts and Grades at Undergraduate degree are independent .

Ha: Wearing seat belts and Grades at Undergraduate degree are not independent .

Step 2 : Test statistic

where Oi : observed frequency

Ei : expected frequency

The contingency table ( of observed frequency)

	A or B	C	D or F	Total
Most / Always	1354	428	65	1847
Rarely/ Never	180	125	40	345
Total	1534	553	105	2192

Expected frequency calculation

E(1354) = 1847*1534/2192 = 1292.563

E(180) = 1534- E(1354) = 214.437

etc

The contingency table of expected frequency

	A or B	C	D or F
Most /Always	1292.563	465.963	88.474
Rarely / Never	241.437	87.03695	16.526

Calculation of Chi square

	Oi	Ei	(Oi-Ei)^2/E
	1354	1292.563	2.9202
	180	241.437	15.6335
	428	465.963	3.0929
	125	87.03695	16.5584
	65	88.474	6.2281
	40	16.526	33.3431
Sum			77.7763

Thus

77.7763

Step 3 . Comparison

degrees of freedom = (2-1)*(3-1) = 2

Note : degrees of freedom = ( number of rows -1) *( number of columns-1)

Critical value of chi square at 0.05 with 2 df

5.991 (from chi square table)

Since calculated value of > 5.991

We reject H0

Step 4: Conclusion

At 5% level of significance , there is sufficient evidence to conclude that wearing seat belts and Grades at Undergraduate degree are not independent .

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