Using 1-PropZTest for Hypothesis Testing

Overview

This lecture explains how to use the 1-PropZTest on a calculator for hypothesis testing and interpret the results to make a statistical decision.

Ensure the conditions of a random sample, large sample, and large population are met before proceeding.
Select 1-PropZTest on your calculator (Stat > Test > Option 5).
Input required values: P₀ (hypothesized population proportion), X (number of successes in the sample), N (sample size), and the alternative hypothesis' inequality.
In the example: P₀ = 0.90, X = 160 (number of successes), N = 185 (sample size), and use "≠" if the alternative hypothesis is "not equal."

The calculator gives a Z test statistic (e.g., 1.59) and a P-value (e.g., 0.11).
Compare the P-value to the significance level (here, α = 0.10) to make a decision.

If P-value > significance level (e.g., 0.11 > 0.10), fail to reject the null hypothesis.
Failing to reject the null means there is not enough evidence to support the alternative hypothesis.
A larger P-value means the sample result is not surprising and is close to what is expected under the null hypothesis.

When failing to reject the null, conclude there is not enough evidence to show a difference in proportions.
Restate the context: There is not enough evidence to say the proportion of Chinese restaurants failing after one year is different from 90%.

1-PropZTest — A statistical test for one sample proportion using the Z statistic.
P₀ — Hypothesized population proportion under the null hypothesis.
X — Number of observed successes in the sample.
N — Total sample size.
P-value — Probability of observing a result as extreme as, or more extreme than, the sample result if the null hypothesis is true.
Significance Level (α) — Threshold for statistical significance, commonly set at 0.05 or 0.10.

Practice running 1-PropZTest with given sample data.
Write conclusion statements by rephrasing the research question.
Review connection between P-value, significance level, and statistical decision.