Have someone can help me to figure out this Math question? A manufacturer of nic

Question

Have someone can help me to figure out this Math question?

A manufacturer of nickel-hydrogen batteries randomly selects 100 nickel plates for test cells, cycles them a specified number of times and determines that 14 of the plates have blistered. Does this data provide compelling evidence for concluding that more than 10% of all plates blister under such circumstances? Use alpha = 0.10. A. State the null and alterative hypotheses. Calculate the test statistic. Find the rejection region. Give a p-value corresponding to the test. Make a conclusion and interpret.

Explanation / Answer

2.

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.1
Ha:   p   >   0.1 [ANSWER]

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b)

As we see, the hypothesized po =   0.1      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.14      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.03      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.333333333   [ANSWER, TEST STATISTIC]

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c)

As this is a 0.1 level, right tailed test, then

Reject Ho when z > 1.28. [ANSWER]

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d)  
          
As this is a    1   tailed test, then, getting the p value,  
          
pvalue =    0.09121122   [ANSWER, P VALUE]

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e)

As P < 0.1, we REJECT THE NULL HYPOTHESIS.      

Hence, there is significant evidence at 0.10 level that the true proportion of blistered plates is greater than 10%. [ANSWER]

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