Question

A production line operation is designed to fill cartons with laundry detergent to a mean weight of 2 kg. A sample of cartons is periodically selected and weighed to determine whether underfilling or overfilling is occurring. If the sample data lead to a conclusion of underfilling or overfilling, the production line will be shut down and adjusted to obtain proper filling.
Data based on simple random sampling are as follows:	1,9	2,08	2,1	2	2,2	1,98	1,8	2,1	2,2	2	2	1,95	2,08	2,1	2,3	2,8
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.

Answer 1

population mean,u = 2

a.

H0: u = 2

H1: u is not equal to 2

b.

if test statistic,z > -Za/2 or z < Za/2 then H0 can not be rejected and conclude that true mean is equal to 2. There is no need to shutdown and readjustment.

c.

if test statistic,z < -Za/2 or z > Za/2 then reject H0 and conclude that true mean is not equal to 2. Sample data lead to a conclusion of underfilling or overfilling, the production line will be shut down and adjusted to obtain proper filling.

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