A polling organization conducted surveys of randomly selected citizens 18 years
ID: 3395248 • Letter: A
Question
A polling organization conducted surveys of randomly selected citizens 18 years old or older and asked whether they support the legalization of medicinal marijuana. The frequencies of reported opinions, by age group, are presented in the table. Test whether the proportion of citizens within each age group who are for or against the legalization of medicinal marijuana are the same at alpha = 0.01. State the hypotheses. Choose the correct answer below. H_0: O_1 = E_1 and O_2 = E_2 and O_3 = E_3 H_1: O_1 not equal to E_1 or O_2 not equal to E_2 or O_3 not equal to E_3 H_0: Opinion and age are independent. H_1: Opinion and age are dependent. H_0: p_1 = p_2 = p_3 H_1: At least one of the proportions is different from the others. Compute the P-value.Explanation / Answer
P value =0.002
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
C3
Total
fo-fe
R1
117
115
87
319
13.1613
8.3548
-21.5161
R2
105
113
145
363
-13.1613
-8.3548
21.5161
Total
222
228
232
682
Expected Frequencies
Column variable
Row variable
C1
C2
C3
Total
(fo-fe)^2/fe
R1
103.8387
106.6452
108.5161
319
1.6682
0.6545
4.2661
R2
118.1613
121.3548
123.4839
363
1.4660
0.5752
3.7490
Total
222
228
232
682
Data
Level of Significance
0.01
Number of Rows
2
Number of Columns
3
Degrees of Freedom
2
Results
Critical Value
9.210
Chi-Square Test Statistic
12.379
p-Value
0.002
Reject the null hypothesis
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
C3
Total
fo-fe
R1
117
115
87
319
13.1613
8.3548
-21.5161
R2
105
113
145
363
-13.1613
-8.3548
21.5161
Total
222
228
232
682
Expected Frequencies
Column variable
Row variable
C1
C2
C3
Total
(fo-fe)^2/fe
R1
103.8387
106.6452
108.5161
319
1.6682
0.6545
4.2661
R2
118.1613
121.3548
123.4839
363
1.4660
0.5752
3.7490
Total
222
228
232
682
Data
Level of Significance
0.01
Number of Rows
2
Number of Columns
3
Degrees of Freedom
2
Results
Critical Value
9.210
Chi-Square Test Statistic
12.379
p-Value
0.002
Reject the null hypothesis