Significance Tests for Proportions

Front

What is the significance level in hypothesis testing?

Back

The significance level, denoted as alpha (α), is the probability of rejecting the null hypothesis when it is actually true. It is the cutoff for determining what is considered a small probability.

Front

Why do we pool data when finding standard error in significance tests for proportions?

Back

We pool the data because we assume that the proportions (p1 and p2) are equal under the null hypothesis (H0).

Front

What is the null hypothesis (H0) in a significance test?

Back

The null hypothesis (H0) is a statement that there is no effect or no difference, and it serves as the starting point for statistical testing.

Front

Write the null and alternative hypotheses for a test where the current proportion of cracked boards is 16% and the supervisor believes it will be less than 16%.

Back

H0: p = 0.16; Ha: p < 0.16.

Front

What does it mean if the sample proportion is higher than a specified value in hypothesis testing?

Back

It provides evidence to support the alternative hypothesis (Ha) that the true proportion is greater than that specified value.

Front

What is the purpose of a significance test for proportions?

Back

The purpose is to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis based on sample data.

Front

What is a Type I error in hypothesis testing?

Back

A Type I error occurs when the null hypothesis is rejected when it is actually true.

Front

What is a Type II error in hypothesis testing?

Back

A Type II error occurs when the null hypothesis is not rejected when it is actually false.

Front

What is the formula for calculating the standard error of the difference in proportions?

Back

The standard error (SE) is calculated as: SE = sqrt[ p(1-p)(1/n1 + 1/n2) ], where p is the pooled proportion and n1 and n2 are the sample sizes.

Front

What does 'p-value' represent in hypothesis testing?

Back

The p-value represents the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed, assuming the null hypothesis is true.