A furniture manufacturer claims that the mean production cost of a dining chair is \$50. Management wants to test if the cost has increased. What are the Type I & Type II Errors? Which is more serious?

• A. Type I: We conclude that μ > 50 when actually μ = 50.Type II: We conclude that μ = 50 when actually μ > 50.Type I is more serious.
• B. Type I: We conclude that μ = 50 when actually μ > 50.Type II: We conclude that μ > 50 when actually μ = 50.Type I is more serious.
• C. Type I: We conclude that μ > 50 when actually μ = 50.Type II: We conclude that μ = 50 when actually μ > 50.Type II is more serious.
• D. Type I: We conclude that μ = 50 when actually μ > 50.Type II: We conclude that μ > 50 when actually μ = 50.Type II is more serious.

Answer: (C)

Verified step by step guidance

1. Step 1: Define the null hypothesis (H_0) and the alternative hypothesis (H_1). Here, H_0: \(\mu\) = 50 (the mean production cost is \$50), and H_1: \(\mu\) > 50 (the mean production cost has increased).
2. Step 2: Understand Type I Error: This occurs when we reject the null hypothesis even though it is true. In this context, it means concluding that the production cost has increased when it actually has not.
3. Step 3: Understand Type II Error: This occurs when we fail to reject the null hypothesis even though the alternative hypothesis is true. Here, it means concluding that the production cost has not increased when it actually has.
4. Step 4: Consider the consequences of each error: Type I Error might lead to unnecessary changes or investigations, while Type II Error might result in missing an actual increase in costs, potentially affecting profitability.
5. Step 5: Evaluate which error is more serious based on business context: Typically, in cost control, missing an increase (Type II Error) could be more costly, but this depends on the specific impact of each error on the company.