A production line operation is designed to fill cartons with laundry detergent to a mean weight of 32 ounces. A sample of cartons is periodically selected and weighed to determine whether under-filling or overfilling is occurring. If the sample data lead to a conclusion of under-filling or overfilling, the production line will be shut down and adjusted to obtain proper filling. a) Formulate the null and alternative hypotheses that will help in deciding whether to shut down and adjust the production line. b) Comment on the conclusion and the decision when H0 cannot be rejected. c) Comment on the conclusion and the decision when H0 can be rejected.

Step-by-step explanation:

a) The null hypothesis states that

The production line operation fills cartons with laundry detergent to a mean weight of 32 ounces.

H0 : µ = 32

The alternative hypothesis states that

The production line operation overfills or under fills cartons with the laundry detergent to a mean weight of above or below 32 ounces.

Ha : µ ≠ 32

b) when the calculations are done and the p value is determined, then it would be compared with the level of significance

When the significance level is lesser than the p value, we do not reject H0 because there is no sufficient evidence to conclude that the production line operation overfills or under fills cartons.

c) When the significance level is greater than the p value, we would reject H0 because there is sufficient evidence to conclude that the production line operation overfills or under fills cartons.

the figures below are made out of circles, semicircles, quarter … find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). remember that we'll also have to cut whatever areas we get in half, since we're only dealing

step-by-step explanation: