Question

(7) A political party claims that its presidential candidate does not have 50% support in the New England states. To test this claim, a political fact-checking agency took a random sample of 1225 voting-age people from the New England states and found that 685 of them supported that particular candidate. What is a 99% confidence interval for the true, unknown percentage of support for that candidate? From this interval, is the political party's claim believable?

Answer 1

Ans.

Let X denote the ditribution for the proportion of people that support the particular candidate.

Then X~ Binomial proportion(p), Since the sample is taken randomly and npq >10 and we have a large sample size.

Therefore we can say that X~N(P,PQ/n).

Now 99% confidence interval is given by:

But we need to test the claim that the candidate does not have 50% support. Therefore we need to find a left tailed confidence interval.

implies interval will be : P

interval : P (685/1225) -2.33* S.E

interval: P 0.526

From the confidence interval we can see that the value of P is greater than 0.5 or 50%, Therefore the claim of the political party is not valid at 1 % level of significance.