Chapter 09 Section 94 Problem 096SolutionFormulating the nul

Chapter 09, Section 9.4, Problem 096

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.06
Ha:   p   >   0.06
As we see, the hypothesized po =   0.06      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.08      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.015019987      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.331559103      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.091502556      
significance level =    0.02      

Comparing p and the significance value, we   FAIL TO REJECT THE NULL HYPOTHESIS.      

A.

We conclude that the percentage of defective bearings is NOT HIGHER than 0.06. [ANSWER]

  
the machine SHOULD NOT be stopped to make necessary adjustments. [ANSWER]

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B.

If alpha = 0.10, As P < .10, then we REJECT Ho. [ANSWER]

The result DIFFERS FROM the answer in A. [ANSWER]