University Statistics Worksheets: Hypothesis Test Interpretation

📚 Topic Summary

Hypothesis testing is a crucial part of statistics, allowing us to make informed decisions based on sample data. Interpreting the results correctly is key to drawing valid conclusions. This worksheet will guide you through understanding the vocabulary, applying the concepts, and thinking critically about hypothesis test interpretations. Remember, a p-value less than your significance level ($\alpha$) means you reject the null hypothesis!

🧠 Part A: Vocabulary

Match the terms with their definitions:

1. Term: Null Hypothesis
2. Term: Alternative Hypothesis
3. Term: P-value
4. Term: Significance Level ($\alpha$)
5. Term: Type I Error

1. Definition: The probability of observing a test statistic as extreme as, or more extreme than, the statistic obtained from a sample, under the assumption that the null hypothesis is true.
2. Definition: The hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.
3. Definition: The hypothesis that contradicts the null hypothesis.
4. Definition: Rejecting the null hypothesis when it is actually true.
5. Definition: The probability of rejecting the null hypothesis when it is true. Commonly set at 0.05.

Match the term to the correct definition:

✍️ Part B: Fill in the Blanks

Complete the following paragraph with the correct terms:

When performing a hypothesis test, we compare the ______ to the ______. If the ______ is less than the ______, we ______ the null hypothesis. This means that we have sufficient evidence to support the ______. However, there is always a chance of making a ______, which occurs when we reject the null hypothesis when it is actually true.

Word Bank: Alternative Hypothesis, P-value, Significance Level, Type I Error, Reject

🤔 Part C: Critical Thinking

Explain, in your own words, the practical implications of making a Type II error (failing to reject a false null hypothesis) in a business decision scenario. Give a specific example.