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.

$\sqrt{\frac{p(1-p)}{n}}$, 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 $n(1-p) \geq 10$

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

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

Random sampling ensures that the sample is representative of the population, reducing bias and allowing for valid inferences about the population.

Increasing the sample size decreases the standard deviation of the sampling distribution, making the sample statistics more precise estimates of the population parameter.

The CLT states that the sampling distribution of the sample mean will be approximately normal if the sample size is large enough (n ≥ 30), regardless of the shape of the population distribution. This allows us to use normal distribution methods for inference.

Checking conditions ensures that the sampling distribution is valid and that the statistical inferences based on the sample are reliable and accurate.

The 10% condition ensures independence of observations when sampling without replacement. It states that the sample size should be no more than 10% of the population size.