Overview
This lecture explains how to calculate the test statistic and P-value for a two-proportion hypothesis test using the TI-84 calculator, emphasizing the importance of sample data and proper function selection.
Finding the Test Statistic and P-value
- The test statistic measures how unusual or surprising a sample is under the null hypothesis.
- Calculating the statistic by hand is complex and prone to errors, so use your calculator.
- Use the TI-84 calculator's "Stat" button, then select "Tests," and choose "2-PropZTest" (option 6) for these problems.
Why Use 2-PropZTest?
- The "2" in 2-PropZTest means the test compares two populations.
- The "prop" indicates the test is about proportions (fraction or percentage of successes).
- The "Test" part signifies it's a hypothesis test, as learned in chapters 7.5 and 8.
- Example: Comparing infants who got therapy versus those who didn’t.
Entering Sample Data
- X1 and N1 are the number of successes and sample size for group 1 (e.g., X1=377, N1=937).
- X2 and N2 are the number of successes and sample size for group 2 (e.g., X2=431, N2=932).
- These numbers come directly from the problem prompt.
- Use data previously identified when calculating the sample proportions.
Choosing the Inequality
- The required inequality (less than, greater than, not equal) is found in step one of the hypothesis test.
- If the question mentions "lower," use the "less than" option for the alternative hypothesis.
Calculating and Interpreting the P-value
- Hit "Calculate" after entering values to get the P-value.
- If you see a P-value like 4.4E-3, it is 0.0044 as a decimal, indicating a small probability.
- Very small P-values (almost zero) suggest the sample is highly unusual under the null hypothesis.
Key Terms & Definitions
- Test Statistic — A numerical measure of how far the sample result is from the null hypothesis.
- P-value — The probability of observing a sample result as extreme as, or more extreme than, the observed value, assuming the null hypothesis is true.
- 2-PropZTest — A calculator function for comparing proportions from two independent samples.
- X1, N1, X2, N2 — Number of successes and sample sizes from two groups, respectively.
Action Items / Next Steps
- Practice using the TI-84 to perform 2-PropZTest with sample data.
- Refer back to your hypothesis from step one to select the correct alternative hypothesis direction.