Identifying Type I and Type II Errors In Exercises 31–36, describe type I and type II errors for a hypothesis test of the indicated claim.


Video Game Systems A researcher claims that the percentage of U.S. gamers that are women is not 50%.

Verified step by step guidance

1. Understand the null hypothesis (H₀) and the alternative hypothesis (H₁). The null hypothesis (H₀) is that the percentage of U.S. gamers who are women is 50%. The alternative hypothesis (H₁) is that the percentage of U.S. gamers who are women is not 50%.
2. Define a Type I error. A Type I error occurs when the null hypothesis (H₀) is rejected even though it is true. In this case, it would mean concluding that the percentage of U.S. gamers who are women is not 50%, when in reality it is 50%.
3. Define a Type II error. A Type II error occurs when the null hypothesis (H₀) is not rejected even though the alternative hypothesis (H₁) is true. In this case, it would mean failing to conclude that the percentage of U.S. gamers who are women is not 50%, when in reality it is not 50%.
4. Consider the implications of each error. A Type I error might lead to incorrect changes in policies or assumptions about the gaming demographic, while a Type II error might result in missed opportunities to address actual differences in the gaming demographic.
5. Ensure the researcher understands the importance of selecting an appropriate significance level (α) for the hypothesis test. The significance level determines the probability of making a Type I error and should be chosen based on the context and consequences of the study.

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating two competing hypotheses: the null hypothesis (H0), which represents a statement of no effect or no difference, and the alternative hypothesis (H1), which indicates the presence of an effect or difference. In this case, the null hypothesis would state that the percentage of U.S. gamers that are women is 50%, while the alternative would claim it is not.

Type I Error

A Type I error occurs when the null hypothesis is incorrectly rejected when it is actually true. In the context of the given claim, this would mean concluding that the percentage of female gamers is not 50% when, in fact, it is. This type of error is also known as a 'false positive' and is denoted by the significance level (alpha), which is the probability of making this error.

Type II Error

A Type II error happens when the null hypothesis is not rejected when it is false. In this scenario, it would mean failing to recognize that the percentage of female gamers is not 50% when it actually is. This error is referred to as a 'false negative' and is denoted by beta (β), representing the probability of making this error. Understanding both types of errors is crucial for evaluating the reliability of hypothesis tests.