Overview
This lecture explains how to interpret the Z-test statistic by focusing on its sign and magnitude to determine whether a sample is unusual and what that means for hypothesis testing.
Interpreting the Z-Test Statistic
- The Z-test statistic consists of two key parts: its sign and its value (magnitude).
- The sign of the Z-test statistic indicates the relationship between sample proportion (P-hat) and hypothesized proportion (Pā).
- A positive Z-test statistic means P-hat is greater than Pā.
- A negative Z-test statistic means P-hat is less than Pā.
- The location of P-hat relative to Pā can be seen as right (positive Z) or left (negative Z) of the center.
Importance of Z-Test Value
- The value (magnitude) of the Z-test statistic shows how unusual the sample is.
- If Z is less than -2 or greater than 2, the sample is considered unusual (more than two standard errors from the center).
- An unusual sample (|Z| > 2) is evidence against the null hypothesis (Pā).
- If Z is between -2 and 2, the sample is not considered unusual.
- A non-unusual sample (|Z| < 2) means there is not enough evidence to reject the null hypothesis.
Practical Use in Hypothesis Testing
- The main purpose of the test statistic is to assess how far the sample result is from what is expected under the null hypothesis.
- Unusual samples provide evidence to discredit the null hypothesis.
- Typical (not unusual) samples are not strong enough evidence to reject the null.
Key Terms & Definitions
- Z-test statistic ā A value that measures how many standard errors a sample statistic is from the hypothesized population parameter.
- P-hat (šĢ ) ā The sample proportion.
- Pā ā The hypothesized population proportion in the null hypothesis.
- Null hypothesis ā The default assumption that there is no effect or no difference.
Action Items / Next Steps
- Add this summary of Z-test interpretation to your note sheet for exam preparation.