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.

Does this provide compelling evidence for concluding that more than 10% of all plates blister under such circumstances? Use alpha = 0.05.

1.) Calculate the test statistic (z) and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z=______

p-value=_____

2.)  If it is really the case that 16% of all plates blister under these circumstances and a sample size 100 is used, how likely is it that the null hypothesis of part (a) will not be rejected by the 0.05 test? (Round your answer to four decimal places.)

3.) 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 hypothesis of part (a) will not be rejected by the 0.05 test? (Round your answer to four decimal places.)

4.) How many plates would have to be tested to have β(0.16) = 0.10 for the test of part (a)? (Round your answer up to the next whole number.)

Answer 1

1)

sample success x   =	13
sample size          n    =	100
std error   se =√(p*(1-p)/n) =	0.0300
sample proportion p̂ = x/n=	0.1300

test stat z =(p̂-p)/√(p(1-p)/n)=	1.0000
p value                          =	0.1587

2)for n=100:

rejection region: p+z*√p(1-p)/n =	0.1494
P(not be rejected given p=0.16)=P(phat<0.1494)=	P(Z<-0.29)=	0.3859

3) for n=200:

rejection region: p+z*√p(1-p)/n =	0.1349
P(not be rejected given p=0.16)=P(phat<0.1349)=	P(Z<-0.97)=	0.1660

4)

required sample size             =n=

((zα(√po(1-po)+zβ(√pa(1-pa))/(p-po))2=

258