Question

In a local referendum to legalize the sale of beer, voters were surveyed about their opinions on the referendum and their views on the moral issue of selling alcohol beverages. From the contingency table, test at 0.05 alpha whether their moral values are related to their opinion on the referendum:



Opinion on referendum



Drinking is :



For Against Undecided

OK

95

83

21

Tolerated

73

71

18

Immoral

12

46

8



Formulate the H0 and H1
C.V. at alpha 0.05 level of significance
Compute the test value: Chi-square X2
Decision
Interpretation

Answer 1

a) Formulate the H0 and H1

$H_0:$ moral values are independent of the opinion on the referendum.

$H_1:$ moral values are related to the opinion on the referendum.

b) C.V. at alpha 0.05 level of significance

$\chi^2_{(0.05(4))}=9.488$

c) Compute the test value: Chi-square X2

for against undecided total

okay 95 73 12 180

tolerated 83 71 46 200

immoral 21 18 8 47

total 199 162 66 427

the values provided are the observed(O), the expected(E) values are calculated using the formula,

$=\frac{row total*column total}{total observations}$

0bserved Expected x2

95 83.88758782 1.47203785

83 93.20843091 1.118054029

21 21.90398126 0.03730747

73 68.29039813 0.32479456

71 75.87822014 0.313621375

18 17.83138173 0.001594499

12 27.82201405 8.997771627

46 30.91334895 7.362742886

8 7.264637002 0.074437131

$\chi^2=\sum\frac{(O-E)^2}{E}$ =19.702

d) Decision

Reject $H_0$ Since the critical value is less than the test static.

e) Interpretation

Voters moral values are related to their opinions on the referendum.