A political poll based on a random sample of 1,200 likely voters tested to see i
ID: 3153410 • Letter: A
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