Proportions

Samples should consist only of volunteers who are available at convenient times.

Samples should come from pre-determined quotas representing specific segments within each population.

Samples must have been selected independently from each other using random sampling methods.

Samples should include every fifth individual from an ordered list until sample size requirements are met.

Z-score

Chi-square statistic

T-score

F-statistic

100 males and 100 females

10 males and 10 females

1000 males and 1000 females

50 males and 200 females

A smaller p-value leading to rejection of the null hypothesis at common alpha levels.

Observed proportion differences aligning closely with those presupposed by a null hypothesis.

A larger-than-expected standard error relative to estimated proportion differences.

Sample sizes that are exactly equal across groups being compared in a study design.

0.5

0

1

Cannot be determined from the given information

Sum of sample standard deviations (s1 + s2)

Range of individual sample sizes (n1 - n2)

Difference between sample proportions ($\hat{p}_1 - \hat{p}_2$)

Product of the sample means ($\bar{x}_1 \times \bar{x}_2$)

Perform another test using different samples.

Fail to reject the null hypothesis.

Increase your alpha level and retest.

Reject the null hypothesis.

Two-proportions z-test

Paired samples t-test

One-sample t-test

Anova f-test

Pooled sample proportion ($\hat{p}_{\text{pooled}}$)

Merged variance ratio

Joint probability function

Aggregate mean proportion

The evidence against the null hypothesis is strong enough to reject it.

The sample proportions are equal to each other.

The null hypothesis can be accepted with high confidence.

There is a significant increase in one population proportion over the other.