Multiple Choice
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?
9. Hypothesis Testing for One Sample
Type I & Type II Errors
Multiple Choice
Describe a Type I & Type II Error for each scenario.
A computer repair store advertises the average repair cost as \$75 or less.
A
Type I: We conclude the average repair cost is more than \$75 when it's actually \$75 or less.
Type II: We conclude the average repair cost is \$75 or less when it's more than that.
B
Type I: We conclude the average repair cost is more than \$75 when it's actually \$75 or less.
Type II: We conclude the average repair cost is more than \$75 when it's actually \$75 or less.
C
Type I: We conclude the average repair cost is \$75 when it's actually more than \$75.
Type II: We conclude the average repair cost is \$75 or less when it's actually \$75 or less.
D
Type I: We conclude the average repair cost is \$75 or less when it's more than that.
Type II: We conclude the average repair cost is \$75 or less when it's more than that.
Verified step by step guidance1
Step 1: Identify the null hypothesis (H_0) and the alternative hypothesis (H_1) based on the claim. Here, the store claims the average repair cost is \$75 or less, so set up:
\(H_0: \mu \leq 75\) (the average cost is \$75 or less)
\(H_1: \mu > 75\) (the average cost is more than \$75)$.
Step 2: Define a Type I error in this context. A Type I error occurs when we reject the null hypothesis even though it is true. So, it means concluding that the average repair cost is more than \$75 when in reality it is \$75 or less.
Step 3: Define a Type II error in this context. A Type II error happens when we fail to reject the null hypothesis even though the alternative hypothesis is true. So, it means concluding that the average repair cost is \$75 or less when in fact it is more than \$75.
Step 4: Summarize the errors clearly:
- Type I error: Saying the average repair cost is more than \$75 when it is actually \$75 or less.
- Type II error: Saying the average repair cost is \$75 or less when it is actually more than \$75.
Step 5: Understand the business implications of these errors. For example, a Type I error might unfairly damage the store's reputation by suggesting higher costs, while a Type II error might mislead customers about potential higher costs.
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