A poll report released by Quinnipiac University Poll on Octo

A poll report released by Quinnipiac University Poll on October 22, 2015 said that Donald Trump got 20% votes from likely Iowa Republican Caucus participants. Then on November 23, 2015, Quinnipiac released a new report saying that of 574 likely Iowa Republican Caucus participants, 25% voted lor Trump. Suppose the participants were randomly selected. Please conduct a test on whether Trump got more Iowa Republican supporters in November. Use a = 0.05.

Solution

test H0 : proportion of votes Trump will get from lowa Republican Caucus participants = 0.2 ag. H1 : proportion > 0.20..

sample size = n = 574..
sample proportion = 0.25..standard error = [ (0.2) * ( 1 - 0.2) / 574 ] = 0.01669568.....
test statistic = ( 0.25 - 0.20 ) / 0.01669568 = 2.994787..

p-value = 0.001373183...
p-value < alpha = 0.05..

so, we will reject H0 i.e, the null hypothesis!
Indeed , Trump got more lowa Republican supporters in November at alpha = 0.05.....