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.

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?

Answer 1

We will be using one sample T-test for hypothesis testing. First, we need to calculate mean and standard deviation for the dataset provided. Mean and Standard deviation are calculated using MS Excel. Following is the screenshot:

Following are the steps followed for one sample t-Test:

At 0.05 significance level, there is enough evidence to claim that the bags are being underfilled. Thus, machinery should be recalibrated.