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. | |||||||||||||||||
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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