2. 115 points | Previous Answers My Notes A sanitation department is interested

Question

2. 115 points | Previous Answers My Notes A sanitation department is interested in estimating the mean amount of garbage per bin for a bis in the city. In a random sample of 40 bins, the saple mean amount was 51.5 pounds and the sample standard deviation was 3.6 pounds. Construct 95% and 999 confidence intervals for the mean a mount of garbage er bin for all binsin he 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. I d) what is the upper limit of the 99% interval? Give your answer to three decimal places.

Explanation / Answer

a) Critical value at 95% Interval is 2.0227

Margin of Error = (2.0227*3.6)/SQRT(40) = 1.151335

Lower limit of 95% Interval is (51.5-1.15335 = 50.349

So, answer is 50.349

b) Upper limit = 51.5+1.15335 = 52.651

So, answer is 52.651

c) Critical value at 99% Interval is 2.7079

Margin of Error = (2.7079*3.6)/SQRT(40) = 1.5414

Lower limit of 99% Interval is (51.5-1.1.5414 = 49.959

So, answer is 49.959

d) Upper limit = 51.5+1.5414 = 53.041

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