Question

A common characterization of obese individuals is that their body mass index is at least 30 [BMI = weight/(height)², where height is in meters and weight is in kilograms]. An article reported that in a sample of female workers, 266 had BMIs of less than 25, 159 had BMIs that were at least 25 but less than 30, and 120 had BMIs exceeding 30. Is there compelling evidence for concluding that more than 20% of the individuals in the sampled population are obese?

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

z=

P-value=

What is the probability of not concluding that more than 20% of the population is obese when the actual percentage of obese individuals is 23%? (Round your answer to four decimal places.)

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.

z	=
P-value	=

(b) 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.)


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.)


(c) 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.)
plates

Answer 1

Ho: p=	0.2
Ha: p>	0.2

value of test statistic z=(phat-p)/√((p(1-p)/n)=						1.18
p value =						0.1190

b  probability of not concluding that more than 20% of the population is obese when the actual percentage of obese individuals is 23% :

rejection region: p+z*√p(1-p)/n =				0.2282
P(not be rejected given p=0.23)=P(phat<0.2282)=					P(Z<-0.1)=		0.4602

2)

z =(x/n-p)/√(p*(1-p)/n)=				1.00
p value =				0.1587

b)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

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

c)

required sample size             =n=

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

258