Testing Hypotheses

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 parameters 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 = 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 = 0.05?
What is the decision rule?
Calculate the test statistic.
Are the bags indeed being underfilled?
Should machinery be recalibrated?

Due Day 7
Reply to at least 2 of your classmates or your faculty member or address any of the following subjects:

Explain the difference between the Null and Alternate Hypothesis.
Explain the difference between a One- and a Two-tail test.
How do we determine the critical value and why is it important?
What is the test statistic? How is it related to the area of significance?

Be constructive and professional in your responses.