A survey of 200 CEOs finds that 83 of them think that the ec

A survey of 200 CEOs finds that 83 of them think that the economy will improve next year. Is there any evidence that the rate is higher among all CEOs than the 32% reported by the public at large?

Solution

As significance level is not given, we assume it is 0.05.

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.32
Ha:   p   >   0.32
As we see, the hypothesized po =   0.32      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.415      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.032984845      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    2.880110547      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.001987679      
significance level =    0.05      

As P < 0.05, we   REJECT THE NULL HYPOTHESIS.      

Thus, there is significant evidence that the rate is higher among all CEOs than the 32% reported by the public at large. [CONCLUSION]