Hypothesis testing is used in business to test assumptions and theories. These assumptions are tested against the 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, exhaustive collective 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 complaint 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?