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.

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

Step-by-step 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

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

how am i supposed to answer

step-by-step explanation: