a) Diet Habits - A federal report indicated that 27%ofchildrenages 2 to 5 years
ID: 2955462 • Letter: A
Question
a) Diet Habits - A federal report indicated that 27%ofchildrenages 2 to 5 years had a good diet - an increaseoverpreviousyears. How large a sample is needed to estimatethetrueproportion of children with good diets within 2% with95%confidence? b) Lifetimes of disposable cameras - Findthe90%confidence interval for the variance and standard deviationforthelifetime of disposable camera batteries if a sampleof16disposable camera batteries has a standard deviationof2.1months. Assume the variable is normallydistributed. Doyou feel that the lifetimes of the batteriesarerelativelyconsistent ? a) Diet Habits - A federal report indicated that 27%ofchildrenages 2 to 5 years had a good diet - an increaseoverpreviousyears. How large a sample is needed to estimatethetrueproportion of children with good diets within 2% with95%confidence? b) Lifetimes of disposable cameras - Findthe90%confidence interval for the variance and standard deviationforthelifetime of disposable camera batteries if a sampleof16disposable camera batteries has a standard deviationof2.1months. Assume the variable is normallydistributed. Doyou feel that the lifetimes of the batteriesarerelativelyconsistent ?Explanation / Answer
a) Diet Habits - A federal report indicated that 27% ofchildren ages 2 to 5 years had a good diet - an increase overprevious years. How large a sample is needed to estimate thetrue proportion of children with good diets within 2% with 95%confidence ? we take P( (absolute value of(â-a)/ab/n) <2 ) = .95So we take 2 ( ab/n)=.02 we plug in .27 for a and .73 forb 2( .27x.73/n)=.02 .27x.73/n=.01 .1971/n =.01 square both sides and get .1971/n=.0001 n=.1971/.0001 n=1971 n=1971 b) Lifetimes of disposable cameras - Find the 90%confidence interval for the variance and standard deviation for thelifetime of disposable camera batteries if a sample of 16disposable camera batteries has a standard deviation of 2.1months. Assume the variable is normally distributed. Doyou feel that the lifetimes of the batteries are relativelyconsistent ? n=16s.d.=2.1 we take P( (absolute value of(â-a)/ab/n) <1.64 ) = .90
1.64=a(1-a)/16)
square both sides 2.69= a (1-a)/16 2.69x16=a(1-a) 43.03= a-a^2 a^2-a+43.06=0 factor using quadratic formula if you need to simplifymore. factor using quadratic formula if you need to simplifymore.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.