Question

In: Statistics and Probability

A public opinion poll surveyed a simple random sample of 1000 voters. Respondents were classified by...

A public opinion poll surveyed a simple random sample of 1000 voters. Respondents were classified by gender (male or female) and by voting preference (Republican, Democrat, or Independent). Results are shown in the contingency table below.

                                                VOTING PREFERENCES

                                                Rep        Dem      Ind         Row Total

Male                                      350         075         25           450

Female                                 275         240         35           550

Column Total                     625         315         60           1000

Is there a gender gap? D3 the men's voting preferences differ significantly from the women's preferences? Use a 0.05 level of significance.

Answers should be in word format please

Solutions

Expert Solution

Solution:

Let us use Chi-square test for independence to analyze the result.

The observed frequency counts is as follows:

Voting Preferences
Rep Dem Ind Row total
Male 350 75 25 450
Female 275 240 35 550
Column Total 625 315 60 1000

Step 1:State the null and alternative hypothesis.

Ho:Gender and voting preferences are independent.

Ha:Gender and voting preferences are not independent.

Step 2:Determination of degree of freedom, the expected frequency count and test statistics.

  • Degree of freedom(df)

df=(r-1)*(c-1)=(2-1)*(3-1)=1*2=2

  • Expected frequency count

Formula to find expected frequency count=(nr*nc)/n where nr= row total, nc=column total and n=total sample size

Expected frequency count
Rep Dem Ind Row total
Male (450*625)/1000=281.25 (450*315)/1000=141.75 (450*60)/1000=27 450
Female (550*625)/1000=343.75 (550*315)/1000=173.25 (550*60)/1000=33 550
Column Total 625 315 60 1000
  • Test statistics

Formula to find test statistics is given as follows:

X2=(O-E)2/ E

Rep Dem Ind
Male (350-281.25)2/281.25=16.81 (75-141.75)2/141.75=31.43 (25-27)2/27=0.15
Female (275-343.75)2/343.75=13.5 (240-173.25)2/173.25=25.72 (35-33)2/33=0.12

X2=16.81+31.43+0.15+13.5+25.72+0.12=87.98

  • Determination of critical value for df=2 and =0.05

X2 Critical value=5.991

  • Interpretation

Since X2 observed value=87.98 is greater than X2 critical value, we reject the null hypothesis and conclude that the gender and voting preferences are not independent.

orchestra answered 2 years ago
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