Hypothesis Testing

Question

You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly different from 0.39. You use a significance level of .      

     

You obtain a sample of size  in which there are 66 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

sample proportion (phat) = 66/229 = 0.288

z = (0.288 - 0.39)/sqrt(0.39*0.61/228) = -3.158

since a two-sided test:

p-value = P(|z| > 3.158)

= P(z < -3.158) + P(z > 3.158).

= 2 * P(z < -3.158) =~ 2*0.0008 = 0.0016 (since normal distribution is symmetric)