A polling organization conducted surveys of randomly selecte

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.

Solution

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