Question

The following data come from a study designed to investigate drinking problems among college students. In 1983, a group of students were asked whether they had ever driven an automobile while drinking. In 1987, after the legal drinking age was raised, a different group of college students were asked the same question.

Drove While Drinking	Year	Total
	1983                       1987
Yes No	1250                         991 1387                       1666	2241 3053
Total	2637                       2657	5294

Use the chi-square test to evaluate the null hypothesis that population proportions of students who drove while drinking are the same in the two calendar years. Use = 0.05. Show all hypothesis testing steps

Answer 1

null hypothesis: Ho:  population proportions of students who drove while drinking are the same in the two calendar years

alternate hypothesis:Ha: population proportions of students who drove while drinking are different in the two calendar years

degree of freedom =(row-1)*(column-1)=(2-1)*(2-1)=1

for 1 degree of freedom and 0.05 level rejection region >3.841

applying chi square test:

Observed	Oi	1983	1987	Total
	Yes	1250	991	2241
	No	1387	1666	3053
	Total	2637	2657	5294
Expected	Ei=?row*?column/?total	1983	1987	Total
	Yes	1116.2669	1124.733	2241
	No	1520.733	1532.267	3053
	Total	2637	2657	5294
chi square	=(Oi-Ei)2/Ei	1983	1987	Total
	Yes	16.022	15.901	31.923
	No	11.760	11.672	23.432
	Total	27.782	27.573	55.355

here as test statitic 55.355 falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude at 0.05 level that  population proportions of students who drove while drinking are different in the two calendar years