Overview
This lecture reviews how to perform the 1-PropZTest for hypothesis testing, focusing on identifying correct input values and interpreting the Z test statistic and P-value.
Inputs for 1-PropZTest
- P0 is the null hypothesis proportion (status quo value) used for comparison.
- x is the number of successes from your sample (in this example, 186).
- n is the total sample size (in this example, 312).
- The inequality used depends on the hypothesis; in this case, it is a "greater than" test.
Performing the 1-PropZTest
- Enter P0, x, n, and the inequality into the calculator or software.
- The example uses P0 = 0.5, x = 186, n = 312, and a "greater than" alternative.
- The Z test statistic result is 3.39.
- The P-value obtained is 3.4 E-4, or 0.0034.
Interpreting the Results
- A P-value shown as "E" with a negative exponent (e.g., E-4) means the value is very close to zero.
- The Z test statistic tells you how many standard errors the sample proportion is from P0 (here, 3.39 above the center).
- The P-value represents the probability of observing a sample as extreme as the one obtained, given the null is true; very small values suggest strong evidence against the null.
Connection to Hypothesis Testing Steps
- Steps for using 1-PropZTest directly align with step three of the hypothesis test process outlined in Section 8.1.
- No need to create new processes for these steps—apply what was learned in Section 8.1.
Key Terms & Definitions
- 1-PropZTest — a statistical test used to compare a sample proportion to a hypothesized proportion under the normal approximation.
- P0 — the hypothesized (null) population proportion.
- x — number of observed successes in the sample.
- n — total sample size.
- Z test statistic — indicates how many standard errors the sample proportion is from the hypothesized proportion.
- P-value — probability of obtaining a test statistic as extreme as observed, if the null hypothesis is true.
Action Items / Next Steps
- Practice using 1-PropZTest with sample data and interpret the results.
- Review Section 8.1 for step-by-step hypothesis testing procedures.