Question

# 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.

-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?

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