Section 10.2

Hypothesis Tests for a Population Proportion

Use Z-tests to make decisions about population proportions based on sample data.

The Logic of Hypothesis Testing

Testing is based on the sampling distribution of .

Core Logic: If the observed sample proportion is highly unlikely under , we reject .

Model Requirements

Random sample or randomized experiment

(sample ≤ 5% of population)

Test Statistic

Use (the hypothesized proportion) in the standard error formula.

Classical & P-Value Approaches

Classical Approach

Compare to critical values ( or ). Reject if in the rejection region.

P-Value Approach

If P-value < , reject . P-value = probability of result as extreme or more.

Hypothesis Test Calculator

Hypothesis Test Calculator for Population Proportion

Perform Z-tests to make decisions about population proportions

Successes (x)

Sample Size (n)

Hypothesized p₀

Significance (α)

Alternative Hypothesis

Hypotheses

Null:

Alternative:

Requirements Met

Calculations

Sample Proportion

Standard Error

Test Statistic

Rejection Region Visualization

Classical Approach

Critical Region: z < -1.960 or z > 1.960

z₀ = 2.0755 is in rejection region

P-Value Approach

P-value = 0.0379

P-value < α = 0.05

Reject H₀

At the α = 0.05 significance level, there is sufficient evidence to conclude that the population proportion differs from 0.35.

Common Pitfalls

Using in Standard Error

Use (not ) for hypothesis tests.

Ignoring Requirements

Always verify first.

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