The following data come from a study designed to investigate drinking problems a
ID: 3295031 • Letter: T
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 1897
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. Do not use any statistiacal software (i.e., Minitab, Excel, etc.) or calculators.
Drove While
Drinking
Year
Total
1983 1897
Yes
No
1250 991
1387 1666
2241
3053
Total
2637 2657
5294
Explanation / Answer
here 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.
for 0.05 level and ((row-1)*(column-1)=(2-1)*(2-1)=1) degree of freedom critical value =3.841
as we know that expected value =(row total*column total)/grand total
and chi square value for a cell =(Observed -Expected value)2/Expected value
therefore from above formulas:
from above chi stat =55.355
as chi square test stat is higher then critical value we reject null hypothesis.
We have sufficient evidence to conclude that population proportions of students who drove while drinking are different in the two calendar years.
O 1983 1897 Total Yes 1250 991 2241 No 1387 1666 3053 Total 2637 2657 5294 E=rowtotal*column total/grand total 1983 1897 Total Yes 1116.27 1124.73 2241 No 1520.73 1532.27 3053 Total 2637 2657 5294 =(O-E)^2/E 1983 1897 Total Yes 16.0217 15.9011 31.923 No 11.760 11.672 23.432 Total 27.782 27.573 55.355Related Questions
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