Decide whether to reject or fail to reject the null hypothes

Decide whether to reject or fail to reject the null hypothesis.

An environmental agency recently claimed more than 28% of consumers have stopped buying a certain product because of environmental concerns. In a random sample of 1050

consumers, you find 40% have stopped buying the product. At alphaequals=0.04,

What is the standardized test statistic?

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.28
Ha:   p   >   0.28

As we see, the hypothesized po =   0.28      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.4      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.013856406      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    8.660254038   [ANSWER]