hey bestie Identifying the null (H0) and alternative (H1 or Ha) hypotheses is the crucial first step in any hypothesis test. Think of it like setting up a legal case:
The Core Idea:
Null Hypothesis (H0): This is the "status quo," the assumption of no effect, no difference, or no relationship. It's what you assume is true until proven otherwise. It always contains a statement of equality (e.g., =, ≤, ≥).
Alternative Hypothesis (H1 or Ha): This is your research hypothesis, the claim you are trying to find evidence for. It directly contradicts the null hypothesis and states there is an effect, a difference, or a relationship. It will always contain an inequality (e.g., =, <, >).
Here’s how to identify them in a question, with examples:
- Look for the “Claim” or “Research Question”:
The alternative hypothesis (H1) is usually what the researcher suspects or is trying to prove. The null hypothesis (H0) is the opposite of that claim.
Example 1: Does a new drug reduce blood pressure?
What is the researcher trying to prove? That the new drug reduces blood pressure.
Alternative Hypothesis (H1): The new drug reduces blood pressure (or the mean blood pressure after taking the drug is less than before).
Mathematically: μafter<μbefore (or μ<some value)
Null Hypothesis (H0): The new drug has no effect on blood pressure (or the mean blood pressure after taking the drug is equal to or greater than before).
Mathematically: μafter≥μbefore (or μ≥some value)
2. Look for Keywords Indicating “No Difference” or “Equality”:
Phrases like “no effect,” “no difference,” “is equal to,” “is the same as,” “is at least,” or “is no more than” often point to the null hypothesis.
Example 2: Is the average height of male students 175 cm?
What's the established or assumed value? 175 cm.
Null Hypothesis (H0): The average height of male students is 175 cm.
Mathematically: μ=175 cm
Alternative Hypothesis (H1): The average height of male students is not 175 cm.
Mathematically: μ=175 cm (This is a two-tailed test, as it doesn't specify if it's greater or less than.)
3. Look for Keywords Indicating a “Difference” or “Direction”:
Phrases like “is different from,” “has increased,” “has decreased,” “is more than,” “is less than,” “is not equal to” often indicate the alternative hypothesis.
Example 3: A company claims that less than 5% of its products are defective.
What is the company claiming? Less than 5% are defective. This is what they want to show is true.
Alternative Hypothesis (H1): The proportion of defective products is less than 5%.
Mathematically: p<0.05
Null Hypothesis (H0): The proportion of defective products is equal to or greater than 5%.
Mathematically: p≥0.05
Key Rules to Remember:
H0 always includes an equality. It will have =, ≤, or ≥.
H1 never includes an equality. It will have =, <, or >.
They are mutually exclusive and exhaustive. Only one can be true, and together they cover all possibilities.
Hypotheses are about the population parameters, not the sample statistics. So you'll use symbols like μ (mean), p (proportion), or σ (standard deviation), not xˉ or p^.
You test the null hypothesis. The goal of hypothesis testing is to gather enough evidence to reject the null hypothesis in favor of the alternative. If you don't have enough evidence to reject H0, you "fail to reject" it – you never "accept" the null hypothesis.
By following these guidelines and looking for the keywords, you’ll be able to correctly formulate your null and alternative hypotheses!