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?
(1) What information do we obtain from the null hypothesis? What information do we obtain from the alternate hypothesis?
(2) What do we mean when we refer to the critical value? Explain your answer with regard to the decision rule.
(3) How do you calculate the test statistics with Excel for either the z or t statistic?