Discussion

Consider the following scenario: An industrial seller of grass seeds packages its product in 50-pound bags. A customer has recently filed a complained alleging that the bags are underfilled. A production manager randomly samples a batch and measures the following weights:

Weight, (lbs)

45.6 49.5
47.7 46.7
47.6 48.8
50.5 48.6
50.2 51.5
46.9 50.2
47.8 49.9
49.3 49.8
53.1 49.3
49.5 50.1

To determine whether the bags are indeed being underfilled by the machinery, the manager must conduct a test of mean with a significance level α = 0.05.

In a minimum of 175 words, respond to the following:

State appropriate null (Ho) and alternative (H1) hypotheses.
What is the critical value if we work with a significant level α = 0.05?
What is the decision rule?
Calculate the test statistic.
Are the bags indeed being underfilled?
Should machinery be recalibrated?