Significance Level
Definition
The significance level, also known as alpha (α), determines how much evidence we need to reject the null hypothesis. It represents the probability of making a Type I error.
Analogy
Imagine you are buying a new phone and want to make sure it works properly. The significance level is like your tolerance for defects - if you set it too low, you might end up rejecting phones that are perfectly fine; if you set it too high, you might accept faulty phones.
Related terms
P-value: The probability of obtaining results as extreme as observed data, assuming the null hypothesis is true.
Confidence Interval: A range of values within which we estimate an unknown population parameter lies with a certain level of confidence.
One-tailed Test: A statistical test where deviations from the expected outcome can only occur in one direction.
"Significance Level" appears in:
Study guides (9)
AP Statistics - 6.7 Potential Errors When Performing Tests
AP Statistics - 6.10 Setting Up a Test for the Difference of Two Population Proportions
AP Statistics - 6.11 Carrying Out a Test for the Difference of Two Population Proportions
AP Statistics - 7.4 Setting Up a Test for a Population Mean
AP Statistics - 7.5 Carrying Out a Test for a Population Mean
AP Statistics - 7.9 Carrying Out a Test for the Difference of Two Population Means
AP Statistics - 7.10 Skills Focus: Selecting, Implementing, and Communicating Inference Procedures
AP Statistics - 8.3 Carrying Out a Chi Square Goodness of Fit Test
AP Statistics - 9.5 Carrying Out a Test for the Slope of a Regression Model
Additional resources (1)
Practice Questions (20+)
- What is the purpose of using a significance level (e.g., 0.05) in a two-sample t-test?
- What is the significance level commonly used in hypothesis testing?
- For a chi-squared test with a chosen significance level of 0.05, which p-value will NOT allow us to reject the null hypothesis?
- Which of the following is not a commonly used significance level in a chi-square goodness of fit test?
- If the p-value in a chi-square goodness of fit test is less than the chosen significance level, what can be concluded about the null hypothesis?
- If the p-value is less than the significance level, what is the conclusion regarding the null hypothesis?
- What is the appropriate conclusion based on the following scenario? The p-value is 0.03, and the significance level is 0.05.
- What is the appropriate conclusion based on the following scenario? The p-value is 0.15, and the significance level is 0.10.
- What is the significance level in hypothesis testing?
- What does it mean if the p-value is exactly equal to the significance level?
- In a hypothesis test, the p-value is calculated to be 0.18. What is the appropriate conclusion at a significance level of α = 0.10?
- In a hypothesis test, the calculated p-value is 0.07. What is the appropriate conclusion at a significance level of α = 0.05?
- In hypothesis testing, if the significance level is set at 0.05, what is the probability of a Type I error?
- What is the significance level in hypothesis testing?
- In a hypothesis test, if the p-value is less than the significance level, what should you do?
- What is the significance level (alpha) in a hypothesis test?
- What is the most common significance level used in research?
- How does setting a significance level that is too low affect the risk of errors?
- What is the complement of the significance level in relation to a confidence interval?
- What is the significance level commonly used to determine whether to reject the null hypothesis?
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