A survey of 200 CEOs finds that 126 of them think that the e

A survey of 200 CEOs finds that 126 of them think that the economy will improve next year. Is there evidence that the rate is higher among all CEOs than the 56% reported by the public at large? Find the standard deviation of the sample proportion based on the null hypothesis. Find the z-statistic. Does the z-statistic seem like a particularly large or small value?

Solution

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.56
Ha:   p   >   0.56

As we see, the hypothesized po =   0.56      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.63      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.035099858   [ANSWER, PART A]

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B)

          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.994310088   [ANSWER, PART B]  

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c)

This seems to be a large value, as for a right tailed 0.05 level test, the critical value is just 1.645.