A manufacturer of nickel-hydrogen batteries randomly selects 100 nickel plates f

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 13 of the plates have blistered. (a) Does this provide compelling evidence for concluding that more than 10% of all plates blister under such circumstances? State and test the appropriate hypotheses using a significance level of 0.05. If it is really the case that 16% of all plates blister under these circumstances and a sample size 200 is used, how likely is it that the null hypotheses will not be rejected?

Explanation / Answer

a)here null hypothesis:Ho: p=0.1

alternate hypothesis: Ha: p>0.10

for n=100 ; std error =(p(1-p)/n)1/2 =0.03

phat=(13/100)=0.13

therefore test stat z=(phat-p)/std error =(0.13-0.1)/0.03=1

for above test stat ; p value =0.1587

as p value is greater then 0.05 ; we fail to reject null hypothesis.

we do not have sufficient evidence to conclude that more then 10% of all plates blister under such circumstances.

b)

here p=0.1 ; n=200

therfore std error ==(p(1-p)/n)1/2 = 0.0212

for 0.05 level; critical value z=1.645

therefore crtiical value for rejection =p + z*std error =0.1+1.645*0.0212=0.1349

for true proportion po =0.16 ; n=200

std error =(p(1-p)/n)1/2 = 0.0259

therefore probability to reject null hypothesis =P(P>0.1349)=1-P(P<0.1349)=1-P(Z<(0.1349-0.16)/0.0259)

=1-P(Z<-0.9685)=1-0.1664=0.8336

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