#18. A quality-control engineer wants to estimate the mean fill weight of boxes

Question

#18. A quality-control engineer wants to estimate the mean fill weight of boxes that have been filled with cereal by a certain machine on a certain day. He draws a simple random sample of 80 boxes from the population of boxes that have been filled by that machine on that day. He computes the sample mean fill weight to be 11.35 oz and the sample standard deviation to bes-1oz. How many boxes must be sampled to obtain a 98% confidence interval of width 0.015 oz? #19. Why do we use the term confidence interval rather than probability interval?

Explanation / Answer

Answer

#18

Z value at 98%CI is equal to 2.33

We know.;

E= Z × {(s÷sq.root "n")}

Here E=0.015 ; Z= 2.33 ; s=0.1

Hence

n= ( Z× S÷E)^2

=241.284

Boxes 242 approx.

#19

Confidence intervals are used in hypothesis testing as well as for estimating population characteristics from sample characteristics .

As uncertainity is associated while we try to estimate the population from sample statistics ,we use confidence intervals not probability intervals.

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