Question

Dairy Fresh produces ice cream sold under the Dairy Fresh brand in the East. The production process is highly automated. The filling machine for 64oz. cartons is good, but not perfect. There is some variation in the actual amount of ice cream that goes into a 64oz. carton. In fact, it is known that the filling amounts are normally distributed with a standard deviation of .5oz. Management wants to make sure that the filling machine operates correctly. They would have to take corrective action if there is indication that the machine is not operating properly. To monitor the filling process, the production manager selects 25 cartons of ice cream at the end of each day. At the end of a particular day, the sample of 25 cartons resulted in a sample mean of 63.85oz. Perform all hypothesis testing steps to determine if the machine is operating properly at a 5% significance level.

Answer 1

H₀: = 64

H₁: 64

The test statistic z = ()/()

                            = (63.85 - 64)/(0.5/)

                            = -1.5

P-value = 2 * P(Z < -1.5)

             = 2 * 0.0668

             = 0.1336

Since the P-value is greater than the significance level, so we should not reject the null hypothesis.

So at 5% significance level there is sufficient evidence to conclude that the machine is operating properly.