Printable Exercises: Null and Alternative Hypotheses for Statistics Students

📚 Topic Summary

In statistical hypothesis testing, the null hypothesis ($H_0$) represents a statement of no effect or no difference, which we aim to disprove. The alternative hypothesis ($H_1$ or $H_a$) represents the statement we are trying to find evidence for, suggesting a specific effect or difference. The goal is to gather data and assess whether the evidence is strong enough to reject the null hypothesis in favor of the alternative.

For example, if we want to test if a new drug is effective, the null hypothesis might be that the drug has no effect, while the alternative hypothesis is that the drug does have an effect. We then collect data to see if we can reject the 'no effect' claim.

🔤 Part A: Vocabulary

Match the terms with their definitions:

1. Term: Null Hypothesis
2. Term: Alternative Hypothesis
3. Term: Significance Level
4. Term: P-value
5. Term: Hypothesis Testing

Definitions (Unordered):

1. The probability of observing a test statistic as extreme as, or more extreme than, the result obtained, assuming the null hypothesis is true.
2. A statement of 'no effect' or 'no difference' that we try to disprove.
3. The process of evaluating evidence to support or reject a claim about a population.
4. The hypothesis that contradicts the null hypothesis, suggesting a specific effect or difference.
5. The probability of rejecting the null hypothesis when it is actually true (Type I error).

✍️ Part B: Fill in the Blanks

Complete the following paragraph with the correct terms:

In __________, we start with a __________ which assumes there is no effect. The __________ represents what we are trying to find evidence for. We use a __________ to determine the threshold for rejecting the null hypothesis. The __________ helps us decide whether to reject the null hypothesis.

🤔 Part C: Critical Thinking

Explain, in your own words, why it is important to formulate both a null and an alternative hypothesis before conducting a statistical test. Provide an example of a situation where clearly defining these hypotheses is crucial for accurate decision-making.