Hypothesis testing is used in business to test assumptions and theories. These assumptions are tested against evidence provided by actual, observed data. A statistical hypothesis is a statement about the value of a population parameter that we are interested in. Hypothesis testing is a process followed to arrive at a decision between 2 competing, mutually exclusive, collective exhaustive statements about the parameter's value.

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)

45.649.5

47.746.7

47.648.8

50.548.6

50.251.5

46.950.2

47.849.9

49.349.8

53.149.3

49.550.1

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

Respond 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 underfilled?
• Should machinery be recalibrated?