Null Hypothesis
Definition
The null hypothesis is a statement of no effect or relationship between variables in a statistical analysis. It assumes that any observed differences or associations are due to random chance.
Analogy
Imagine you're accused of cheating on a test, and the null hypothesis would be "You did not cheat." To prove your innocence, you need strong evidence against this null hypothesis. If there isn't enough evidence, we fail to reject the null hypothesis and assume you didn't cheat (innocent until proven guilty).
Related terms
Alternative Hypothesis: The alternative hypothesis is the opposite of the null hypothesis and suggests that there is an effect or relationship between variables.
Type II Error: Type II error occurs when we fail to reject a false null hypothesis, meaning we mistakenly conclude there is no effect or relationship when there actually is one.
One-tailed Test: In a one-tailed test, we focus on detecting an effect in only one direction (e.g., greater than or less than).
"Null Hypothesis" appears in:
Subjects (1)
Study guides (12)
AP Statistics - 6.5 Interpreting p-Values
AP Statistics - 6.6 Concluding a Test for a Population Proportion
AP Statistics - 6.7 Potential Errors When Performing Tests
AP Statistics - 6.8 Confidence Intervals for the Difference of Two Proportions
AP Statistics - 6.9 Justifying a Claim Based on a Confidence Interval for a Difference of 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 - 7.8 Setting Up a Test for the Difference of Two Population Means
AP Statistics - 7.9 Carrying Out a Test for the Difference of Two Population Means
AP Statistics - 8.2 Setting Up a Chi Square Goodness of Fit Test
AP Statistics - 9.4 Setting Up a Test for the Slope of a Regression Model
AP Statistics - 9.5 Carrying Out a Test for the Slope of a Regression Model
Additional resources (2)
Practice Questions (14)
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?
In a chi-square goodness of fit test, the null hypothesis states that the observed frequency distribution is:
If the chi-square statistic is greater than the critical value in a chi-square goodness of fit test, what can be concluded about the null hypothesis?
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?
In a chi-square goodness of fit test, when the observed chi-square statistic is 15.72 and the critical value is 12.59, what can be concluded about the null hypothesis?
For a chi-squared test for independence, the null hypothesis states that:
Which would be a correct null hypothesis for a chi-square independence test about gender and job experience?
Which of the following represents the null hypothesis (H0) for a t-test of the slope?
What is the distribution of the slope estimate when the assumptions of a linear regression model are satisfied and the null hypothesis is true?
If the p-value is less than the significance level, what is the conclusion regarding the null hypothesis?
When can we reject the null hypothesis in a two-sample z-interval?
The null hypothesis in a two-sample t-test states that:
Which statement accurately describes the null hypothesis in a significance test for the difference in two population proportions?
In a one-proportion z-test, the null hypothesis is always written as:
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