Explain the concept of variance addition when comparing two proportions.
When dealing with differences, variances ALWAYS add. To find the standard deviation, take the square root of the combined variance.
Explain the purpose of checking the Large Counts condition.
To confirm that the sampling distribution of the difference in sample proportions is approximately normal.
What does the sampling distribution for the difference in sample proportions represent?
It represents all possible differences in sample proportions you could obtain if you repeated the sampling process many times.
Why is it important to understand the sampling distribution?
It allows us to make inferences about the true difference in population proportions based on sample data.
Describe the Central Limit Theorem (CLT) in the context of proportions.
With sufficiently large sample sizes, the sampling distribution of the difference in sample proportions will be approximately normal, regardless of the shape of the original populations.
What is the formula for the standard deviation of the difference in sample proportions?
$$\sqrt{\frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}}$$
Formula for the mean of the sampling distribution of the difference in sample proportions.
$$\mu = p_1 - p_2$$
What is the formula for calculating a confidence interval?
Point Estimate ± (Critical Value * Standard Error)
How do you calculate the sample proportion?
$$\hat{p} = \frac{number \ of \ successes}{sample \ size}$$
How to calculate standard error of the sampling distribution of the difference in sample proportions.
$$\sqrt{\frac{\hat{p_1}(1-\hat{p_1})}{n_1} + \frac{\hat{p_2}(1-\hat{p_2})}{n_2}}$$
What are the differences between standard deviation and variance?
Standard Deviation: Measures the spread of data around the mean, in original units. | Variance: Measures the average squared distance from the mean, in squared units.
What are the differences between a one-sample z-test and a two-sample z-test for proportions?
One-Sample: Compares a sample proportion to a known population proportion. | Two-Sample: Compares the proportions of two independent samples.
What are the differences between the Central Limit Theorem and the Large Counts condition?
Central Limit Theorem: Applies to means (quantitative data), stating that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases. | Large Counts Condition: Applies to proportions (categorical data), ensuring the sampling distribution of the sample proportion is approximately normal.
Differentiate between a point estimate and a confidence interval.
Point Estimate: A single value used to estimate a population parameter. | Confidence Interval: A range of values likely to contain the population parameter, providing a measure of uncertainty.
What are the differences between Type I and Type II error?
Type I error: Rejecting a true null hypothesis (false positive). | Type II error: Failing to reject a false null hypothesis (false negative).
