Math Problem Statement

A researcher looks at the mean salaries of male and female electricians and decides based on the evidence that there is no difference between the two groups. The researcher could have made a Type I Error or Type II Error in drawing this conclusion.

Solution

In this question, a researcher concludes that there is no difference between the mean salaries of male and female electricians based on the evidence. The question is asking whether this could lead to a Type I Error or a Type II Error.

To determine this, let's break down both types of errors:

  1. Type I Error (False Positive): This occurs when the null hypothesis is true, but it is incorrectly rejected. In this case, the null hypothesis would be that "there is no difference in salaries between male and female electricians." If the researcher concluded that there is a difference when in fact there is none, this would be a Type I Error.

  2. Type II Error (False Negative): This occurs when the null hypothesis is false, but it is incorrectly accepted. If the researcher concluded that "there is no difference" when in reality there is a difference between the salaries of male and female electricians, it would be a Type II Error.

Since the researcher concluded that there is no difference between the groups, the error would be a Type II Error if, in reality, there is a difference between the groups but it was not detected.

Thus, the answer to this question is Type II Error.

Do you need further details or have any other questions?

Here are 5 related questions you might want to explore:

  1. What conditions lead to a Type I Error in hypothesis testing?
  2. How can you minimize the risk of committing a Type II Error?
  3. What is the relationship between Type I and Type II Errors in terms of significance level (α\alpha) and power (1β1-\beta)?
  4. Can the size of the sample affect the probability of committing a Type II Error?
  5. What role does the p-value play in avoiding a Type I Error?

Tip: Increasing your sample size can reduce the likelihood of a Type II Error, as it provides more data to detect any existing differences.

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Type I Error
Type II Error
Statistical Inference

Formulas

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Theorems

Null Hypothesis
Alternative Hypothesis

Suitable Grade Level

Grades 11-12, Undergraduate