Question

You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly more than 0.6. You use a significance level of α=0.001.

H0:p=0.6
H1:p>0.6

You obtain a sample of size n=734 in which there are 470 successes.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p =0.6

Ha : p >0.6

= x / n = 470/734=0.6403

P0 = 0.6

1 - P0 = 1-0.6=0.4

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.6403 -0.6/ [(0.6*0.4) /734 ]

Z= 2.227

P(z >2.227 ) = 1 - P(z <2.227 ) = 1-0.987=0.0130

P-value = 0.0130