University of Phoenix Calculate the Test Statistic Questions

I’m working on a data analytics writing question and need an explanation to help me study.

Consider the following scenario. An industrial seller of grass seeds packages its product in 50-pound bags. A customer has recently filed a complaint alleging the bags are under filled. 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 has to conduct a test of mean with a significance level ? = 0.05.

Write a response to the following:

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