Question

4. * (5 points). This sample of 10 data points are taken from quality-control work at a flour mill. The bags of flour are supposed to be sixteen ounces in weight, with a variance no greater than 0.2 ounces2. Are the bag-filling machines filling the bags within the 0.2 ounce 2 tolerance, or does the machinery need adjusting? 15.8 15.6 16 16.2 15.7 15.9 16.1 16.2 16.3 16.1

Answer 1

∑x = 159.9 , ∑x² = 2557.29

n = 10

Variance, s² = (Ʃx² - (Ʃx)²/n)/(n-1) = (2557.29-(159.9)²/10)/(10-1) = 0.0543

Null and alternative hypothesis:

Hₒ : σ² = 0.2

H₁ : σ² ≠ 0.2

Test statistic:

χ² = (n-1)s² / σ² = (10 - 1)0.0543/0.2 = 2.4450

Degree of freedom:

Df = n -1 = 10 - 1 = 9

p-value = 2*(1-CHISQ.DIST.RT(2.445, 9)) = 0.0354

Decision:

p-value < 0.05, Reject the null hypothesis.

There is enough evidence to conclude that the bag filling machine filling the bag is not in the tolerance limit.

The machinery need adjusting.