A dean of a business school wants to know if the proportion

A dean of a business school wants to know if the proportion of graduates who use statistical inference within the first year of graduation is greater than 0.6. A survey of 436 graduates resulted in 181 saying that they used statistical inference within the first year of graduation. Calculate the test statistic for the hypothesis specified above, to two decimal places.

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.6
Ha:   p   <   0.6

As we see, the hypothesized po =   0.6      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.415137615      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.023461857      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -7.879273512= -7.88 [ANSWER]