HW 6-2 A sanitation department is interested in estimating the mean amount of ga

Question

HW 6-2

A sanitation department is interested in estimating the mean amount of garbage per bin for all bins in the city. In a random sample of 40 bins, the sample mean amount was 51.5 pounds and the sample standard deviation was 3.6 pounds. Construct 95% and 99% confidence intervals for the mean amount of garbage per bin for all bins in the city.

a) What is the lower limit of the 95% interval? Give your answer to three decimal places.  

b) What is the upper limit of the 95% interval? Give your answer to three decimal places.  

c) What is the lower limit of the 99% interval? Give your answer to three decimal places.  

d) What is the upper limit of the 99% interval? Give your answer to three decimal places.  

e) Consider the claim that the mean amount of garbage per bin is 52.791 pounds. Is the following statement true or false? The decision about the claim would depend on whether we use a 95% or 99% confidence interval.

TrueFalse

Explanation / Answer

z value for 95% is given as 1.96 and z for 99% is 2.576

Mean is 51.5 and s is 3.6. thus standard error is s/sqrt(N)=3.6/sqrt(40)=0.5692

a) lower limit for 95% is mean-se*z =51.5-0.5692*1.96=50.384

b) upper limit is mean+se*z =51.5+0.5692*1.96=52.616

c) lower limit for 99% =51.5-0.5692*2.576=50.034

d) upper limit =51.5+0.5692*2.576=52.966

e)  claim is mean amount of garbage per bin which is 52.791 pounds, yes it will depend on the interval.So TRUE

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