2. A production-line operation is designed to put 32 ounces of laundry detergent

Question

2. A production-line operation is designed to put 32 ounces of laundry detergent in each carton. A random sample of cartons is periodically selected and weighed to determine whether under-filling or over-filling is occurring. If the sample data lead to a conclusion of either under-filling or over-filling the production line will be shut down and adjusted to obtain proper filling. a. State the null and alternative hypotheses that will help in deciding whether to shut down and adjust the production line b. What does it mean to "Fail to Reject" the null hypothesis in this test (include whether or not the production line should be shut down and adjusted)? c. What does it mean to "Reject" the null hypothesis in this test (include whether or not the production line should be shut down and adjusted)? d. Describe a Type I Error for this situation; be specific, meaning use information about shutting down the production line e. Describe a Type II Error for this situation; be specific, meaning use information about shutting down the production line

Explanation / Answer

Part a

The required null and alternative hypotheses are given as below:

Null hypothesis: H0: The average weight of laundry detergent in each carton is 32 ounces.

Alternative hypothesis: Ha: The average weight of laundry detergent in each carton is other than 32 ounces.

Symbolically, null and alternative hypotheses are given as below:

H0: µ = 32 Vs Ha: µ 32

This is a two tailed test.

Part b

Fail to reject the null hypothesis in this test means there is sufficient evidence to conclude that average weight of laundry detergent in each carton is 32 ounces. The production line should not be shut down and adjusted.

Part c

Reject the null hypothesis in this test means there is insufficient evidence to conclude that average weight of laundry detergent in each carton is 32 ounces. There is sufficient evidence to conclude that average weight of laundry detergent in each carton is other than 32 ounces. The production line should be shut down and adjusted.

Part d

Type I error is the error when we reject the null hypothesis when it is true. For the given scenario, type I error is defined as the probability of rejecting the null hypothesis that average weight of laundry detergent in each carton is 32 ounces, when actually average weight is 32 ounces.

Part e

Type II error is the probability of do not rejecting the null hypothesis when it is not true. For the given scenario, type II error is the probability of do not rejecting the null hypothesis that average weight of laundry detergent in each carton is 32 ounces, when actually average weight is not 32 ounces.

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