A political poll based on a random sample of 1,200 likely voters tested to see i

Question

A political poll based on a random sample of 1,200 likely voters tested to see if gender has an influence on candidate preference.   The participants were asked if they planned to vote for Candidate A or Candidate B in the upcoming election. Results are shown in the contingency table below: (need answers for F and G)

Candidate you will vote for

Gender

Candidate A

Candidate B

Male

250

300

Female

350

300

What proportion of females will vote for Candidate B?

P=300 / 1200

C. What proportion of males will vote for Candidate B?

      P = 300 / 1200

D. What is the “relative risk” of the voting preference for Candidate B for females compared to males?

      Rel = 300 / 300 = 1

E. What is the “relative risk” of the voting preference for Candidate B for males compared to females?

Rel = 300 / 300 =1

F. How would you interpret the value that you computed in part E for a friend with no knowledge of statistics?

G. Conduct a chi-square test of independence to determine if there is evidence of a relationship between gender and voting preference for a candidate in the population. Assume that this sample is a representative sample of the population. Use the five-step hypothesis testing procedure labeling each of your steps.   (worth 5 of 10 points)

Step 1:

Step 2:

Step 3:

Step 4:

            Step 5:

Candidate you will vote for

Gender

Candidate A

Candidate B

Male

250

300

Female

350

300

Explanation / Answer

F) The Relative Risk (RR) is 1. This suggest no difference or little difference in risk for voting prefernce for candidate B for males compared to females.

G) Step1. State hypotheses:

H0: Gender and voting prefernce are independent.

H1: Gender and voting prefernce are associated.

Step2. Assumptions:

Counted data collection: Count for two categorized variables are available. Independence assumption: The people in this study are likely to be independent. Randomization condition: This is an experiment, therefore, data are randomized. 10% condition: The total 1200 people are less than 10% all voting population comprising male and female. Expected cell frequency: Expected cell frequency is at least 5. [look followingtable for expected frequency]

Formula for expected freqency:(Row marginal*column marginal)/total

Step3. Compute Chi-square.

X^2=Summation (Observed-Expected)^2/Expected

=(250-2750^2/275+(300-275)^/275+(350-325)^/325+(300-325)^2/325

=8.392

Step4. Compute p value.

At df=1 [df=(r-1)(c-1)=(2-1)(2-1)=1], the p value is 0.004.

Step5. Conclusion.

The p value is less than alpha=0.05. Therefore, reject null hypothesis to conclude that there is association among gender and voting prefernce.

Candidate A Candidate B Male 275 [(550*600)/1200] 275 Female 325 325

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