Answer to Question #121984 in Statistics and Probability for Jerald Ebol

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

Given contingency table :

Given is Observed values table :

TOTAL

95 73 12 180

83 71 46 200

21 18 8 47

TOTAL 199 162 66 427

Step 1: State the hypothesis:

Ho: Opinions on the referendum and their views on the moral issue of selling alcohol beverages are independent of each other.

H1: Opinions on the referendum and their views on the moral issue of selling alcohol beverages are not independent of each other

Step 2:

Expected values table

Expected values are calculated as follows:

Expected value = (row total *column total )/grand total

For example :

For value 95, expected value E= 180*199/427=83.89

For observed value 73,E= 180*162/427=68.29

similarly we find for all values and we get following expected value table.

(83.89)    (68.29)    (27.82)  

 (93.21)   (75.88)    (30.91)  

 (21.90)   (17.83)  (7.26)  

Test statistic= O is the observed value and E is expected value

$\Sigma\frac{(O-E)^2}{E}$

=1.472+1.118+0.037+0.325+0.314+0.002+8.998+7.363+0.074=19.702

From Observed values and E expected values from above two tables , and formula we get test statistic=19.7024

Step 3: CV at 0.05 level of significance , df= (r-1)(c-1)= 4, is

9.488.

step 4:

Test statistic is greater than CV. Hence null hypothesis is rejected.

Step 5: Hence there is no evidence to say that opinions on the referendum and their views on the moral issue of selling alcohol beverages are independent of each other