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.
9. Hypothesis Testing for One Sample
Type I & Type II Errors
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Describe a Type I & Type II Error for each scenario.
A snack company guarantees that each bag contains at least 200 g of chips.
A
Type I: We conclude that some bags don't have at least when they all do.
Type II: We conclude that some bags don't have at least 200 g when they all do.
B
Type I: We conclude all bags have at least when some don't
Type II: We conclude all bags have at least when some don't
C
Type I: We conclude that all bags have at least when some don't.
Type II: We conclude that some bags don't have at least when they all do.
D
Type I: We conclude that some bags don't have at least when they all do.
Type II: We conclude all bags have at least when some don't.
Verified step by step guidance1
Step 1: Identify the null hypothesis (H_0) and the alternative hypothesis (H_a) for the scenario. Here, the snack company guarantees each bag contains at least 200 g of chips, so we set:
\[ H_0: \text{Each bag contains at least 200 g} \]
\[ H_a: \text{Some bags contain less than 200 g} \]
Step 2: Understand what a Type I error means in hypothesis testing. A Type I error occurs when we reject the null hypothesis even though it is true. In this context, it means concluding that some bags have less than 200 g when in reality all bags meet the 200 g guarantee.
Step 3: Understand what a Type II error means. A Type II error happens when we fail to reject the null hypothesis even though the alternative hypothesis is true. Here, it means concluding that all bags have at least 200 g when some bags actually have less than 200 g.
Step 4: Clearly state the Type I error for this problem: "Concluding that some bags don't have at least 200 g when in fact all bags do."
Step 5: Clearly state the Type II error for this problem: "Concluding that all bags have at least 200 g when in fact some bags do not."
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