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 the appropriate hypotheses using a significance level of 0.05. b) If it is really the case that 16% of all plates blister under these circumstances and a sample size 200 used, how likely is it that the null hypothesis will not be rejected?

Explanation / Answer

a) here null hypothesis: Ho:p<=0.1

alternate hypothesis:Ha:p>0.1

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

phat=13/100=0.13

hence 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 level of significance ; we can not reject null hypothesis.

we have insufficient evidence to conclude that more then 10% of all plates blister under such circumstances,

b) here n=200 ; p=0.1

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

for 0.05 level of signficance critical value of z=1.645

therefore critical value for rejecttion of null hypothesis =p+z*std error =0.1349

for true p0 =0.16

therefore std error =0.0259

hence for rejection 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

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.