Revise later
SpaceTo flip
If confident
All Flashcards
Explain the concept of interpreting a confidence interval in context.
State the confidence level, refer to the population parameter (difference in population proportions), and relate the interpretation to the specific scenario.
Explain how a confidence interval can be used to test a claim about the difference in two population proportions.
If the confidence interval contains zero, we fail to reject the null hypothesis. If it does not contain zero, we reject the null hypothesis.
Explain the meaning of a 95% confidence level.
If we were to take many samples and build a confidence interval from each sample, then approximately 95% of those intervals would contain the true population difference.
What does it mean if a 95% confidence interval for the difference of two proportions is (-0.1, 0.2)?
We are 95% confident that the true difference in population proportions lies between -0.1 and 0.2. Because the interval contains 0, there may be no difference between the two population proportions.
What is the role of 'zero' in hypothesis testing using confidence intervals for the difference of two proportions?
Zero represents the absence of a difference between the two proportions. Its inclusion or exclusion from the confidence interval determines whether we reject the null hypothesis.
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?
$(\hat{p}_1 - \hat{p}_2) \pm z^* \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}$
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.