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?