Describe a Type I & Type II Error for each scenario.
$\left(A\right)$ 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 $200g$ 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 $200g$ when some don'tType II: We conclude all bags have at least $200g$ when some don't
• C. Type I: We conclude that all bags have at least $200g$ when some don't.Type II: We conclude that some bags don't have at least $200g$ when they all do.
• D. Type I: We conclude that some bags don't have at least $200g$ when they all do.Type II: We conclude all bags have at least $200g$ when some don't.

Answer: (D)

Verified step by step guidance

1. 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: \[ H_0: \text{Each bag contains at least 200 g} \] \[ H_a: \text{Some bags contain less than 200 g} \]
2. 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.
3. 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.
4. 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."
5. 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."