How yo solve and how to do confidence interval for one tail test ??

Question

News agencies are taking polls to try to figure out the general population’s opinions on an election poll. Suppose a

female candidate wants to see how much percentage of people will vote for her. Suppose a survey of 500 randomly

selected respondents shows that 125 of them will vote for her in the next election. If we want to test if there is sufficient

evidence in the data to claim that the proportion of the population that will not vote for this candidate is greater than 0.8

𝛼 = 0.05,

(1) Test the hypothesis using the fixed-𝛼 approach.

(2) Can you answer the same hypothesis test question in part (1) by constructing an appropriate confidence interval? Do

you draw the same conclusion?

Answer 1

Part 1). The tricky part of this problem is to decide how you want to state the null & alternative hypothesis. Generally, you want to disprove the null hypothesis and this means you use the alternative to state what you are hoping to 'prove' from the data you collect. It's important to take the time to formulate the null hypothesis you're interested in. To do that, the first step is to consider the question you want to answer. the problem above states:

We want to test if there is sufficient evidence in the data to claim that the proportion of the population that will not vote for this candidate is greater than 0.8, or, more susinctly: Will the population proportion that votes 'NO' be ≥ 0.80. The thing to notice here is that we need to calculate that number, since the problem tells us proportion that voted 'YES' , we need to use the information given to calculate the proportion that votes 'NO', so we need to do a little extra work, to find the proportion of the sample that will vote 'NO', which is simply the total number (500)-the number that voted 'YES' (125), 500-125=375. Now we can state our 2 hypotheses:

Our null hypothesis is:H_o=p₀ ≤ 0.08. and corresponding alternative hypothesis is H_a =p >0.08.

Everything else follows as you would normally do: calculate the appropriate test statistic, using an α=0.05 (or 0.05/2 for a one-tailed test), find the critical value using the tables that are likely in the back of your book, evaluate your hypotheses, interpret your results, etc.

Part 2). Can you answer the same hypothesis test question in part (1) by constructing an appropriate confidence interval? YES

Do you draw the same conclusion? you need to do those calculations & answer for yourself. I'm not allowed to do your homework, just help you understand how, which I think I've done. Good Luck!