Math Problem Statement

The sample suggests that the food is safe, but it actually is not safe. What type of error is this in a hypothesis test?

Solution

The question provided is asking about hypothesis testing errors, particularly the type of error described when a sample incorrectly suggests that the food is safe, while it is actually not safe.

Given the hypotheses:

  • H0H_0: The food is safe.
  • HaH_a: The food is not safe.

The situation described in the question is: "The sample suggests that the food is safe, but it actually is not safe."

This is a Type II error. In a Type II error, the null hypothesis (H0H_0) is not rejected when it should be (i.e., the test fails to detect that the alternative hypothesis is true). Here, the test concludes that the food is safe (H0H_0), but in reality, the food is not safe (HaH_a is true).

Would you like a detailed explanation of hypothesis testing errors or have any other questions?

Here are five related questions:

  1. What is a Type I error in hypothesis testing?
  2. How can we reduce the likelihood of making a Type II error?
  3. What is the relationship between the significance level (α\alpha) and Type I errors?
  4. How do power and sample size affect Type II errors?
  5. What are the practical implications of Type I and Type II errors in quality control?

Tip: Increasing the sample size of a test can reduce the probability of a Type II error by providing more data to support correct decision-making.

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Type I and Type II Errors

Formulas

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Theorems

Hypothesis Testing Errors

Suitable Grade Level

College level statistics