10.1: The Null and Alternate Hypothesis and Errors in Hypothesis Testing Flashcards
What is the null hypothesis in hypothesis testing?
The null hypothesis (H₀) is the statement being tested in hypothesis testing, which is assumed true until evidence indicates otherwise.
It is given the benefit of the doubt and is not rejected unless there is convincing evidence that it is false.
What symbol is used to denote the null hypothesis?
The null hypothesis is denoted by H₀.
What is the alternative hypothesis in hypothesis testing?
The alternative hypothesis (H₁ or Hₐ) represents a new claim or effect we suspect might be true and is accepted only if there is convincing sample evidence in its support.
What symbol is used to denote the alternative hypothesis?
The alternative hypothesis is denoted by Hₐ or H₁.
How are the null and alternative hypotheses related in the context of research?
The null hypothesis (H₀) states there is no effect or no difference, and it’s the opposite of the alternative hypothesis (Hₐ), which is the research hypothesis that suggests there is an effect or a difference.
What is a one-sided alternative hypothesis? Give an example.
A one-sided alternative hypothesis specifies a direction of an effect.
Example: Hₐ: μ > 50, where μ represents a population mean, and the claim is that μ is greater than 50.
What is a two-sided alternative hypothesis? Give an example.
A two-sided alternative hypothesis does not specify a direction but rather that the values are not equal to a specific value.
Example: Hₐ: μ ≠ 330, suggesting the mean is not equal to 330 without specifying if it’s higher or lower.
When setting up a null hypothesis, what type of equality is typically used?
The null hypothesis typically involves an equality statement, such as H₀: μ ≤ 50 or H₀: μ = 330, suggesting that the parameter is either equal to, less than, or greater than a specific value until proven otherwise.
How do the roles of the null and alternative hypotheses compare to the American criminal court system?
In the American criminal court system, the null hypothesis is analogous to the presumption of the defendant’s innocence, and the alternative hypothesis is like the claim that the defendant is guilty, which needs strong evidence to be accepted.
Why is the burden of proof on the alternative hypothesis in hypothesis testing?
The burden of proof is on the alternative hypothesis because it represents a new claim or assertion that goes against the status quo, which is represented by the null hypothesis.
What does it mean when we do not reject the null hypothesis?
When we do not reject the null hypothesis (H₀), it means that there is not enough sample evidence to support the alternative hypothesis (Hₐ).
This is analogous to a “not guilty” verdict in a legal system, implying a lack of evidence rather than proving innocence.
What is a Type I error in hypothesis testing?
A Type I error occurs when we incorrectly reject a true null hypothesis (H₀).
It is the error of finding an effect or difference when there is none.
What is a Type II error in hypothesis testing?
A Type II error happens when we fail to reject a false null hypothesis (H₀).
It is the error of not finding an effect or difference when one actually exists.
What symbols represent the probabilities of Type I and Type II errors?
The probability of a Type I error is denoted by alpha (α), and the probability of a Type II error is denoted by beta (β).
How do we control the probability of making a Type I error?
We control the probability of making a Type I error by setting the significance level (α), which is the threshold for rejecting the null hypothesis (H₀).
