What are the differences between a sample proportion and a population proportion?
Sample Proportion: Calculated from a subset of the population, used to estimate the population proportion. | Population Proportion: The true proportion for the entire population, usually unknown.
What are the differences between interpreting a confidence interval and making a conclusion in a hypothesis test?
Confidence Interval: Provides a range of plausible values for the true difference. | Hypothesis Test: Determines whether there is sufficient evidence to reject the null hypothesis based on the interval.
What are the differences between a null and alternative hypothesis?
Null Hypothesis: Assumes no difference between population proportions. | Alternative Hypothesis: Suggests there is a significant difference between population proportions.
What is the formula for the standard error of the difference between two sample proportions?
$SE = \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}$
What is the general formula for a confidence interval?
Estimate ± (Critical Value) * (Standard Error)
How to calculate the confidence interval for the difference of two proportions?
$(\hat{p}_1 - \hat{p}_2) \pm z^* \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}$
Define confidence interval.
A range of plausible values for the true difference between two population proportions.
What is a population proportion?
The true proportion of individuals with a certain characteristic in the entire group of interest.
Define confidence level.
The probability that a confidence interval will contain the true population parameter if repeated samples are taken.
What is a null hypothesis?
A statement of no effect or no difference that we aim to disprove with statistical evidence.
Define alternative hypothesis.
A statement that contradicts the null hypothesis, suggesting a specific effect or difference.
What are confounding variables?
Extraneous factors that can influence the results of a study, potentially leading to incorrect conclusions about the relationship between variables.
