B. It ain’t easy bein’ green A dealer in recycled paper places empty trailers at

Question

B. It ain’t easy bein’ green

A dealer in recycled paper places empty trailers at various sites. The trailers are gradually filled by individuals

who bring in old newspapers and magazines, and are picked up on several schedules. One such schedule

involves pickup every second week. This schedule is desirable if the average amount of recycled paper is more

than 1600 cubic feet per 2-week period. The dealer’s records for eighteen 2-week periods show the following

volumes (in cubic feet) at a particular site:

recycle=c(1935,1556,1752,1969,1804,1842,1994,1810,1827,1725,2003,1499,1809,1795,1622,1620,1777,2035)

The mean and standard deviation are as follows: ¯X = 1721.6 and s = 154.5

(a) In constructing confidence intervals, would we use z? or t? in this situation? Briefly explain why you

would use one instead of the other.

(b) Estimate the true mean weight of recycled paper with 95% confidence. Interpret.

Explanation / Answer

a) ere as we do not know population std deviaiton as well shape of population distribution and also sample size is less then 30 therfore we would use t distribution

b)

here std error of mean =std deviaiton/(n)1/2 =154.5/(18)1/2 =36.416

for (n-1=17) degree of freedom and 95% CI ; critical value of t =2.1098

hence 95% CI true mean weight =sample mean -/+ t*Std error =1644.769 to 1798.431

above interval gives 95% confidence to contain true mean weight of recycled paper

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