A sportscaster claims that, in general, the home team wins more than 50% of games in the National Football League (NFL). During the 2016 NFL regular season, the home team won 147 of the 256 games played. Is there significant evidence of a "home field advantage" in professional football (i.e. the home team wins more than 50% of their games)? Consider the data from 2016 to represent a random sample of games from the population of all NFL games ever played. Assume a = 0.05.
a) Conduct a full hypothesis test by following the steps below. Enter an answer for each of these steps in your document.
i. State the null and alternative hypotheses using correct notation.
ii. State the significance level for this problem.
iii. Check the three conditions of the Central Limit Theorem that allow you to use the standard Normal test statistic using one complete sentence for each condition. Show work for the numerical calculation.
iv. Calculate the test statistic "by-hand." Show the work necessary to obtain the value by typing your work and provide the resulting test statistic.
v. Calculate the p-value using the standard Normal table and provide the answer.
vi. State whether you reject or do not reject the null hypothesis and your reason for your answer in one sentence.
vii. State your conclusion in context of the problem (i.e. interpret your results and/or answer the question being posed) in one or two complete sentences.