Question

A quality control manager is concerned about variability of the net weight of his company’s individual yogurt cups. To check the consistency, he takes a random sample of sixteen 6-ounce yogurt cups and finds the mean of the sampled weights to be 5.85 ounces and the sample standard deviation to be 0.2 ounce.

Requried:
a. Test the hypotheses H0: µ ≥ 6 Ha: µ < 6 at the 5% level of significance. Assume the population of yogurt-cup net weights is approximately normally distributed.
b. Based on the results of the test, will the manager be satisfied that the company is not under-filling its cups?
c. State the decision rule, the test statistic, and the manager’s decision.

Answer 1

H₀ should be rejected, yogurt cups are under-filling, the manager has to check the process

Explanation:

Normal distribution and n < 30. We must use t-student test.

a) If it is required to test H₀ μ >= 6 Hₐ μ < 6 is a one tail test (left-tail)

At α = 5 % α = 0,05 and n = 16 then degree of freedom is n -1

df = 15 find t(c) = - 1,753

μ = 5,85 and s = 0,2 ( sample mean and standard deviation respectevily)

T compute t(s)

t(s) = ( μ - μ₀ ) / s/√n

t(s) = ( 5,85 - 6 ) /0,2/√16

t(s) = - 0,15*4/0,2

t(s) = - 3

t(s) < t(c) -3 < - 1,753

Then t(s) is in the rejection region we reject H₀. There is enough evidence to claim the yogurt cups are under-filling.

Manager has to check on the process