Thirteen tons of cheese is stored in some old gypsum mines, including “22-pound”

Question

Thirteen tons of cheese is stored in some old gypsum mines, including “22-pound” wheels (label weight). A random sample of n = 9 of these wheels yielded the following weights in pounds: 21.50 18.95 18.55 19.40 19.15 22.35 22.90 22.20 23.10 Assuming that the distribution of the weights of the wheels of cheese is N(µ ?2 ) find:

(1) an unbiased point estimate of µ

(2) an unbiased point estimate of ?2

(3) a 90% confidence interval for µ

(4) a 95% confidence interval for ?2

(5) a 95% confidence interval for ?.

Explanation / Answer

1)

mean

20.9 AVERAGE

2)

sd^2

3.4538 VAR.S

3)

mean= 20.9

sd= 1.858426754

u= 400

n= 9

alpha= 0.1

t(a/2,n-1)

t(0.1/2,9-1)

1.860

CI = mean +- t(a/2,n-1)*(sd/sqrt(n))

lower = 20.9 - 1.86*(1.85842675400458/sqrt(9))= 19.75

upper = 20.9 + 1.86*(1.85842675400458/sqrt(9))= 22.05

4)

chisq(1-a/2,n-1)

chisq(1-0.05/2,9-1)

=CHIINV(1-0.05/2,9-1)

2.1797

chisq(a/2,n-1)

=chisq(0.05/2,9-1)

=CHIINV(1-0.05,9-1)

2.7326

lower limit for popn varince

(n-1)*s^2 / chisq(a/2,n-1)

=(9-1)*3.4538/2.7326

10.111396

upper limit for popn variance

(n-1)*s^2 / chisq(1-a/2,n-1)

=(9-1)*3.4538/2.1797

12.67624

5)

CI for popn s.d.

lower= =SQRT(10.111396) = 3.1798

upper= =SQRT(12.67624) = 3.5604

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