In: Statistics and Probability
Problem 1 – Election poll
The incumbent governor of a province in Indonesia believes that he
will succeed in the upcoming regional election in winning more than
50% of the votes amongst the 13,324,525 registered voters. A random
sample of 1,000 voters were selected. 510 people stated that they
would vote for the governor. Estimate with 99% confidence the true
proportion of voters who would vote for the governor.
a) You are recently hired as a junior data analyst working for the
governor’s office. Specify the appropriate formula you would use to
solve the problem. Provide a brief reason why you chose the
formula.
b) Obtain the 99% confidence interval estimate of the true
proportion of voters who would vote for the governor. Display
working.
c) Provide an interpretation of the answers you obtained in part b)
in the context of the problem.
d) Present brief statements of two or three sentences to the
governor’s office with regard to the possibility of him winning the
election on the basis of the interval estimation conducted. Is it
very much conclusive that he will win the election? Why?
e) Assuming all of the other variables to do the calculation of confidence interval held constant, what would happen to the width of the interval when a lower sample size is used?