Question

In a recent survey​ conducted, a random sample of adults 18 years of age or older living in a certain country were asked their reaction to the word socialism. In​ addition, the individuals were asked to disclose which political party they most associate with. Results of the survey are given in the table. Complete parts ​(a) through ​(c) below.

_	Democrats	Independents	Republicans
Positive	216	64	158
Negative	270	370	411

(a) Does the evidence suggest individuals within each political affiliation react differently to the word​ "socialism"? Use the

alpha equals 0.05

level of significance.

State the hypotheses.

A.Upper H 0: pSubscript Upper DequalspSubscript Upper RequalspSubscript Upper I

Upper H 1:At least one of the proportions is different from the others.

B.Upper H 0: Political party and reaction are independent.

Upper H 1:Political party and reaction are dependent.

C.Upper H 0:Political party and reaction are dependent.

Upper H 1:Political party and reaction are independent.

D.Upper H 0: OSubscript Upper D equalsESubscript Upper Dand OSubscript Upper R equalsESubscript Upper Rand OSubscript Upper I equalsESubscript Upper I

Upper H 1: At least one mean is different from what is expected.

Compute the​ P-value.

The​ P-value=?

Make the proper conclusion. Choose the correct answer below.

A.Yes​, there is evidence because the​ P-value is greater than alpha.

B.Yes​, there is evidence because the​ P-value is less than alpha.

C.No​, there is no evidence because the​ P-value is greater than alpha.

D.No​, there is no evidence because the​ P-value is less than alpha.

(b) Construct a conditional distribution of reaction by political party.

	Democrats	Independents	Republicans
Positive
Negative

(c) Write a summary about the​ "partisan divide" regarding the reaction to the word​ "socialism."

A.Democrats, Independents, and Republicans all had a majority negative reaction. The proportions are likely to be equal.

B.Republicans and Independents are far more likely to react negatively to the word ​"socialism" than Democrats are. All groups had a majority negative reaction.

C.Democrats are far more likely to react negatively to the word​"socialism" than Independents and Republicans are. All groups had a majority negative reaction.

D.Republicans and Democrats are far more likely to react negatively to the word​ "socialism" than Independentsare. All groups had a majority negative reaction.

Answer 1

Chi-Square Test of independence
	Observed Frequencies
	0
0	DEMOCRAT	INDEPENDT	REPUCLIC				Total
POSITIVE	216	64	158				438
NEGATIVE	270	370	411				1051
Total	486	434	569				1489
	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	DEMOCRAT	INDEPENDT	REPUCLIC				Total
POSITIVE	486*438/1489=142.96	434*438/1489=127.664	569*438/1489=167.375				438
NEGATIVE	486*1051/1489=343.04	434*1051/1489=306.336	569*1051/1489=401.625				1051
Total	486	434	569				1489
	(fo-fe)^2/fe
POSITIVE	37.317	31.748	0.525
NEGATIVE	15.552	13.231	0.219

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   98.591         
              
Level of Significance =   0.05          
Number of Rows =   2          
Number of Columns =   3          
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 3- 1 ) =   2          
              
p-Value =   0.0000   [Excel function: =CHISQ.DIST.RT(χ²,df) ]     
Decision:    p-value < α , Reject Ho          

B.Yes​, there is evidence because the​ P-value is less than alpha.

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