A social scientist is interested in determining if the Ameri

A social scientist is interested in determining if the Americans between the ages of 25 and 44 are becoming more educated as a group. Using the General Social Survey data set, he discovered that, out of 800 individuals in this age bracket surveyed, 303 had an associate’s degree or higher.

Calculate the test statistic for testing the hypothesis that the true proportion of individuals with an associate’s degree or higher is greater than 0.383, the proportion reported by the U. S. Census Bureau, to two decimal places.

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.383
Ha:   p   >   0.383
As we see, the hypothesized po =   0.383      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.37875      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.017186877      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -0.247281687   [ANSWER]