Hypothesis testing is used in business to test assumptions and theories. These assumptions test against the evidence provided by actual, observed data. A statistical hypothesis is a statement about the value of a population parameter. Hypothesis testing is a process to decide between two (2) competing, mutually exclusive, collectively exhaustive declarations about the parameter's value. (Refer to LO 9-1).

Weight, (lbs.)

51.94

52.54

49.78

49.94

48.61

46.74

49.35

50.10

51.13

46.71

51.45

47.77

48.51

48.71

49.67

48.43

50.62

45.65

51.44

50.37

47.63

51.73

51.95

48.48

49.31

48.27

52.31

49.7

47.51

44.98

Aparametercan be the population mean, population proportion, population standard deviation, population variance. We will work primarily with the mean.

Scenario. An industrial seller of grass seeds packs product in 50-pound bags. A customer has recently filed a complaint alleging underweight bags. A production manager randomly sampled a batch and measures the following weights (use Week 4 Discussion Data in Resources below).

To determine whether the machinery is indeed underfilling the bags, the manager will conduct aone-sample t-test of meanswith a significance level = 0.05. The population standard deviation () is unknown. Use a one-tail test to show if the bags are underweight. (Refer to LO 9-7). Use the hypothesis testing steps in Example One-Sample t-Test of Means.

Save time: (a) Reuse and modify Example 1 One-Sample t-Test of Means; (b) Answer the questions in the Excel document.

A. Use a one-tail t-test means

Step 1: State the Hypotheses (Ho, H1)

Step 2: Specify the Decision Rule

Include, the significant level (alpha), with a 95% confidence level

Step 3: Calculate the Test Statistic and p-value

Step 4: Make the Decision

Step 5: Take Action

Are the bags underweight? Should they recalibrate the machinery?

B. The next two questions illustrate a different outcome when using a two-tail test.

B1. Calculate the two-tail t-test statistic and p-value.

B2. Compare the one-tail test p-value to a two-tail test p-value. Which test is most favorable to the production manager (less likely to prove underfilled bags)? Why?