Describe a Type I & Type II Error for each scenario. ( B ) \left(B\right) A computer repair store advertises the average repair cost as $75 or less.

Welcome to the practice. For this problem, just like with part a, we'd like to describe a type one and type two error for this scenario, where the scenario is that a computer repair store advertises the average repair cost as $75 or less. Again, this situation isn't about a population proportion or a population mean, but we don't need to be able to perform the full hypothesis test. We just need our hypothesis, and then we will be able to identify the type one and type two errors. The null hypothesis again is going to be that the initial assumption is true, and the initial assumption is that the computer repair store's advertisement is correct, that the average repair cost is $75 or less. So our null hypothesis here is that the average repair cost is $75 or less. Again, we don't see any sort of information about a specific test being run, so the alternative hypothesis is going to be the opposite of the null hypothesis and the opposite of the average repair cost being $75 or less would be that the average repair cost is more than $75, so that's going to be our alternative hypothesis. As a reminder, a type one error is when we reject a true null hypothesis, so we conclude the alternative hypothesis when the null hypothesis is actually true, or we conclude that the average repair cost is more than $75 when, in actuality, the average repair cost is $75 or less. So that's gonna be our type one error. Again, we conclude the average repair cost is more than $75 when it's actually $75 or less. A type two error is when we fail to reject a false null hypothesis. So we would conclude that the null hypothesis is true, that the average repair cost is $75 or less, when in actuality, the alternative hypothesis would be true, that the average repair cost is more than $75. So our type two error here is that we conclude the average repair cost is $75 or less when it's more than that. Great work.

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9. Hypothesis Testing for One Sample

Type I & Type II Errors

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9. Hypothesis Testing for One Sample

Type I & Type II Errors

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Multiple Choice

Describe a Type I & Type II Error for each scenario.
$(B)$ A computer repair store advertises the average repair cost as \$75 or less.

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.

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.

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.

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.

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Verified step by step guidance

Step 1: Identify the null hypothesis ($H_0$) and the alternative hypothesis ($H_a$) based on the scenario. Here, the store advertises the average repair cost as \$75 or less, so we set $H_0: \mu \leq 75$ and $H_a: \mu > 75$.

Step 2: Understand what a Type I error means in hypothesis testing. A Type I error occurs when we reject the null hypothesis $H_0$ even though it is true. In this context, it means concluding that the average repair cost is more than \$75 when it is actually \$75 or less.

Step 3: Understand what a Type II error means. A Type II error happens when we fail to reject the null hypothesis $H_0$ even though the alternative hypothesis $H_a$ is true. Here, it means concluding that the average repair cost is \$75 or less when it is actually more than \$75.

Step 4: Express the Type I error clearly: "Rejecting $H_0$ (concluding average cost > \$75$) when in reality $\mu \leq 75$."

Step 5: Express the Type II error clearly: "Failing to reject $H_0$ (concluding average cost $\leq 75$) when in reality $\mu > 75$."

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Describe a Type I & Type II Error for each scenario.(B)\left(B\right) A computer repair store advertises the average repair cost as \$75 or less.

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Type I & Type II Errors practice set

Describe a Type I & Type II Error for each scenario.
$(B)$ A computer repair store advertises the average repair cost as \$75 or less.