p-value what is the p value of z

Question

You are conducting a study to see if the proportion of women over 40 who regularly have mammograms is significantly different from 0.39. Your sample data produce the test statistic z=2.37. Find the p-value accurate to 4 decimal places.

Answer 1

Since the purpose of the study is to see if the proportion is "different" from 0.39 this is a two-sided p-value, which means it is the probability of getting a z at least as far from 0 in either direction as the observed z = 2.37.  So  

 

P-value = P(Z < -2.37  or  Z > 2.37)  

            = 2*P(Z < -2.37)  

            = 2*0.0089

            = 0.0178  

 

Note that if the purpose of the study had been to see if the proportion was "higher" (or "lower") then the p-value would have been only 0.0089