Sampling Distribution of Proportions: Deals with categorical data, uses sample proportions, and checks the large counts condition. | Sampling Distribution of Means: Deals with numerical data, uses sample means, and relies on the Central Limit Theorem or a normally distributed population.

One-Sample: Involves making inferences about a single population. | Two-Sample: Involves comparing two populations and requires checking conditions for both samples.

Population Standard Deviation: Measures the variability within the entire population. | Standard Deviation of Sampling Distribution: Measures the variability of sample statistics (like means or proportions) across different samples.

Large Counts: Used for sample proportions, requires at least 10 expected successes and failures. | Central Limit Theorem: Used for sample means, states that the sampling distribution of the sample mean will be approximately normal if the sample size is large enough (n ≥ 30).

Conditions for Proportions: Random, Independence (10% condition), Normality (Large Counts condition). | Conditions for Means: Random, Independence (10% condition), Normality (Population is normal or n ≥ 30).

$\sqrt{\frac{p(1-p)}{n}}$, where p is the population proportion and n is the sample size.

$\frac{\sigma}{\sqrt{n}}$, where σ is the population standard deviation and n is the sample size.

$np \geq 10$ and $n(1-p) \geq 10$

$\sqrt{\frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}}$

$\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}$

A distribution of a statistic (like a sample mean or sample proportion) from all possible samples of the same size from a population.

The distribution of sample proportions calculated from multiple random samples of the same size taken from a population.

The distribution of sample means calculated from multiple random samples of the same size taken from a population.

A theorem stating that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's distribution.

When sampling without replacement, verify that the sample size is no more than 10% of the population size to ensure independence.