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)

45.6     ......................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?