During an election, an exit poll is taken on 400 randomly selected voters and 214 of those polled voted for Candidate "Jim". A majority is needed to win the election. We want to see if we can conclude that the majority will vote for Candidate "Jim" based on our sample proportion from the exit poll. The alternative hypothesis (Ha) is what we are testing to see and the null hypothesis (Ho) is the value that we are testing "against". (See page 402--the null hypothesis is a statement that the parameter takes a particular value, while the alternative hypothesis is that the parameter falls in some alternative range of values). We test to see if we can reject the null hypothesis and conclude the alternative hypothesis.
A)
i) State the null and alternative hypotheses using proper Statistical Notation (p for population proportion).
ii) Is this a one-sided alternative hypothesis (> or <) or a two-sided alternative hypothesis (≠)?
iii) What is the SEo. Show all work.
iv) Calculate your test statistic (we use a Z test statistic with proportions). Show all work.
v) Go to the Z Table in the back of the text and determine the p-value for our Z test statistic value. If we have a > alternative, we want the right-tail p-value. If we have a < alternative, we want the left-tail (cumulative probability) p-value. If we have a ≠ alternative, we want the two-tailed p-value.
vi) What is our conclusion based on the p-value? (Can we declare Candidate "Jim" the winner?) Why?