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

Week 4 Discussion

Considering the scenario provided, the claim or theory to be tested is determining whether the 50-pound bags containing grass seeds are underfilled or not, since a customer complained of having underfilled grass seeds bags. The randomly picked batch presents 20 bags with different weights. Using this claim, the test is whether the mean weight of the grass seeds bags is less than 50 pounds or not. Therefore, the appropriate null hypothesis (H₀) is that the machinery is not underfilling the grass seeds bags, and the mean weight is indeed 50 pounds, which can be represented as H₀: μ= 50. The alternative hypothesis is that the customer’s claim is true, and the machinery is underfilling the grass seed bags, which can be represented as H₁: μ< 50. The null and alternative hypotheses present a one-sided and left tailed test: H₁: μ<μ₀. In a left tailed test, the follower for a test statistics is H₁: μ< the claimed value. The formula used in this case is. Hence, with the significance level being α = 0.05, a degree of freedom of 19 (n-1/20-1=19), the critical value is 0.05,19 = z= -1.729. This means that any score that is left of -1.729 or is less than -1.729 falls in the rejection area.

Thus, the decision rule for this test is that the null hypothesis will be rejected if the static value observed is lower than -1.729, which can be represented as “Reject H₀ when the z-score < -1.729. Using the formula, the observed test statistic is -2.232 (z = -2.232). Using the diagram below, it shows that z= -2.232 falls in the rejection area as z= -2.232< -1.729. This means the null hypothesis that grass seeds bags in the machinery are not under filled is rejected.

The results conclude that there is sufficient evidence to prove the customer’s claim (true alternative hypothesis); YES, the grass seeds are underfilled, and the machinery should be recalibrated.

(Emmert-Streib & Dehmer, 2019).

Reference

Emmert-Streib, F., & Dehmer, M. (2019). Understanding Statistical Hypothesis Testing: The Logic of Statistical Inference. Machine Learning & Knowledge Extraction, 945-961. DOI: 10.3390/make1030054.