Suppose that 500 parts arc tested in manufacturing and 10 ar

Suppose that 500 parts arc tested in manufacturing and 10 arc rejected. Test the hypothesis against Find the P-value. Explain how the question in part (a) could be answered by constructing a 95% onesided confidence interval for p.

Solution

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.03
Ha:   p   <   0.03
As we see, the hypothesized po =   0.03      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.02      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.007628892      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -1.310806263      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.094961613   [ANSWER, P VALUE]

significance level =    0.05      

As P > 0.05, we FAIL TO REJECT THE NULL HYPOTHESIS.  

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B)

We can construct un upper tailed 95% confidence interval in part A. If the upper bound is less than 0.03, then we reject Ho. If the upper bound is greater than 0.03, we fail to reject Ho.