P-Value of of Propotion

Question

A poll taken just prior today finds that 389 of 700 registered voters intend to vote for Jake Anderson for mayor. We want to test Ho: q=0.5 where q represents the proportion of all voters who intend to vote for Jake. Find the p-value. 

This is a question on my practice final and I am so confused. I have no idea where to even start. Help!

Answer 1

The formula for the Z value is ( p--P) divided by the square root of the quantity ( P( 1--P)) / n
Where p is the sample proportion, which is those voting for Jake( 389), divided by the 700 people polled. This is p = 0.5557 .

P is the population proportion with which we are comparing our test statistic. This is 0.5 because we want to determine if Jake has less than or more than half the voters; it is a two tailed test.
n is the number of people polled.
So we have Z = ( p-P) / ((P(1-P) /n)^0.5 = (0.5557-0.5) / (( 0.5(0.5) / 700)^0.5 = 2.948123
This z value gives us a p-value of 0.0016 or 0.16%.

 

This is a two tailed test; therefore, we must multiply this area( probability) by two to get 0.0032 or 0.32%.  If I'm reading the question correctly, you are asking for the null hypothesis to be confirmed( accepted or rejected).  The critical area is 0.05( usually), and we are beyond that at 0.0016( on each side); therefore, we reject the null hypothesis that Jake's proportion is 0.5.  But this is a good thing for Jake because he has a greater proportion than one half.  The chances of Jake being elected is good.