A Find the critical region and make a decision B Calculate t

A) Find the critical region and make a decision.

B) Calculate the P-Value for this test and make a decision.

Solution

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.9
Ha:   p   =/=   0.9
As we see, the hypothesized po =   0.9      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.85      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.009486833      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -5.270462767      

For a two tailed test, 0.05 significance, the rejection region is

z<-1.96 or z>1.96.

As -5.27046 < -1.96, then we REJECT THE NULL HYPOTHESIS.

There is significant evidence that the population proportion of those who are satisfied or very satisfied with a corporation\'s products and services is not 0.9. [CONCLUSION]

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b)

As this is a    2   tailed test, then, getting the p value using technology/table,  
          
p =    0.00000013608      

As P < 0.05, we   REJECT THE NULL HYPOTHESIS.

There is significant evidence that the population proportion of those who are satisfied or very satisfied with a corporation\'s products and services is not 0.9. [CONCLUSION]