AP Statistics Type I and Type II Errors

What is a Type I Error in statistics?

• A Type I Error occurs when a true null hypothesis is rejected. It is also known as a 'false positive.'

• A Type I Error occurs when a false null hypothesis is accepted. It is also known as a 'false negative.'

• A Type I Error occurs when the sample size is too small to draw a conclusion.

• A Type I Error occurs when the data is not normally distributed.

What does it mean to fail to reject the null hypothesis?

• It means there is enough evidence to support the alternative hypothesis.

• It indicates that the null hypothesis is proven to be true.

• It means there is not enough evidence to support the alternative hypothesis, but it does not prove that the null hypothesis is true.

• It suggests that the results are statistically significant.

What is a Type II Error in statistics?

• A Type II Error occurs when a false null hypothesis is not rejected. It is also known as a 'false negative.'

• A Type II Error occurs when a true null hypothesis is rejected, leading to a false positive.

• A Type II Error is when the sample size is too small to detect an effect.

• A Type II Error is when the test fails to produce any results.

What is a confidence interval?

• A method to calculate the mean of a dataset.

• A range of values that is likely to contain the population parameter with a specified level of confidence.

• A statistical test to determine the significance of results.

• A graphical representation of data distribution.

What is a p-value in hypothesis testing?

• A p-value is the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true.

• A p-value indicates the strength of the evidence against the null hypothesis.

• A p-value is the threshold for determining the significance level of a test.

• A p-value represents the probability of the null hypothesis being true.

What is a critical value in hypothesis testing?

• A threshold that determines whether to reject the null hypothesis, based on the significance level and the distribution of the test statistic.

• A value that indicates the mean of the sample data.

• A point at which the test statistic is calculated to determine the p-value.

• A fixed number that is used in all hypothesis tests regardless of the significance level.

What is a null hypothesis (H0)?

• A statement that there is no effect or no difference, and it is the hypothesis that researchers aim to test.

• A hypothesis that predicts a specific outcome or effect.

• A statement that suggests a relationship between two variables.

• A theory that has been proven through extensive research.

What is the significance level (alpha) in hypothesis testing?

• The probability of making a Type II Error.

• The probability of making a Type I Error. It is commonly set at 0.05.

• The threshold for determining statistical significance in a study.

• The level of confidence in the results of a hypothesis test.

What does it mean to reject the null hypothesis?

• It means that the null hypothesis is likely true.

• It means that the evidence suggests the null hypothesis is unlikely to be true, leading to support for the alternative hypothesis.

• It means that the null hypothesis has been proven false.

• It means that the alternative hypothesis is accepted without evidence.

How can sample size affect Type I and Type II errors?

• Larger sample sizes can increase the Type I error rate.

• Larger sample sizes can reduce the likelihood of Type II errors and provide more accurate estimates.

• Sample size has no effect on Type I or Type II errors.

• Smaller sample sizes are always better for reducing errors.