A purchase manager knows that the hardness of castings from any supplier is normally distributed with a mean of 20.25 and SD of 2.5. He picks up 100 samples of castings from any supplier who claims that his castings have heavier hardness and finds the mean hardness 20.50. Test whether the claim of the supplier is tenable.

To test whether the supplier's claim of heavier hardness is tenable, we can perform a hypothesis test using the concepts of quantitative analysis for managerial applications. Specifically, a z-test is appropriate here because the population standard deviation is known, and the sample size is large (n = 100).

### Step 1: Define the Hypotheses

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