Question

Archipelago World News, oldest newspaper in the Archipelago. Poll contacted 2000 randomly generated landline and cell phone numbers of Westopiaresidents during the past week and asked the question:

•Who are you planning on voting for?

Results: 1109 respondents support our candidate.

Conduct a significance test to determine if the poll predicts your candidate will win - that is, the majority of voters will select your candidate.

a) Write the Null and Alternative Hypotheses for this test

b) Check the assumptions necessary for this test to be valid.

c) What is the Test Statistic?

d) What is the P-value? and interpret the P-value

e) What is the 95% confidence interval for p? and interpret this interval

f) How confident are you that your candidate will win the election? and explain

- Very confident will win

- Very confident will lose

- Pretty confident will win

-Pretty confident will lose

g) Does the analysis of the poll predict your candidate will win?

h) Now it's three weeks later and the day of the election. A lot has happened since then, including a lot of negative media coverage on both candidates. Do you still think the conclusions made by you are valid? Explain

Answer 1

• Here X is the random variable denoting the number of supporters during voting.
• The estimated sample proportion is given by =1109/2000=0.5545
• Here we test the claim that where the candidates wins with majority of the supporting votes.
• A) HYPOTHESIS
• Let the null hypothesis be that supporting votes is equal to 50% of the population.
• Vs the alternate hypothesis that the supporting votes is more than 50% of the population so as to win the cadidature
• H0:p=0.5 vs H1:p>0.5.
• B) ASSUMPTIONS
• Here the situation is that of the binomial distribution with n binomial trials with P(success)=p; we observe X success i.e the number of voters.
• Test statistics is X~binomial (n,po) under Ho.
• For large n, use the normal approximation to the binomial (with continuity correction), ie use:
  
• approximately.
• When carrying out tests of this type you can work out whether you need to add or
  subtract the 1/2 in the continuity correction if you remember that you always adjust the
  value of X towards the mean of the distribution under H0. For large values of n, this
  will make little difference unless the test statistic is close to the critical value.
• C) UNDER H0 ,TEST STATISTICS .
• 
• Test statistics with continuity correction.
• =4.896.
• D) P VALUE
• P(X>4.896)=1-P(X<4.896)=1-0.99999=0.00001
• E) CONCLUSION
• The p value obatained is less than 1% significance level .
• Therefore we do have enough evidence to reject null hypothesis
• Therefore we conclude candidates wins with majority of the supporting votes.