Sampling Distributions for Sample Means - AP Statistics

Outliers can skew the sampling distribution. Extreme values affect the distribution's shape.

$s$. Standard notation for sample standard deviation.

Larger sample size increases accuracy. Larger samples reduce sampling error.

$\bar{x}$. Standard symbol for sample mean.

The spread decreases as sample size increases. Variability decreases as sample size increases.

Depends on population shape, not always normal. Small samples retain original population distribution shape.

To allow normal approximation for sample means. Enables statistical inference about population means.

Results in a narrower, more precise sampling distribution. Smaller standard error means more concentrated distribution.

Standard error decreases as $n$ increases. Due to inverse square root relationship with $n$.

As sample size increases, standard error decreases. Standard error is inversely proportional to $\sqrt{n}$.

Variability of a statistic across different samples. Natural variation in statistics from sample to sample.

Sample size $n$ is less than 10% of the population. 10% rule prevents finite population effects.

Approximately normal for large $n$ due to Central Limit Theorem. CLT applies regardless of original population shape.

Estimator equals the population parameter on average. Expected value equals the true population parameter.

An estimator that does not equal the population parameter on average. Expected value differs systematically from true parameter.

Variability decreases as sample size increases. Standard error decreases proportional to $\frac{1}{\sqrt{n}}$.

The sampling distribution is normal. Normal population always produces normal sampling distribution.

Depends on population shape, not always normal. Small samples retain original population distribution shape.

Ensures each sample has an equal chance of selection. Prevents bias and ensures representative sampling.

Adjustment to standard error for small population. Modifies standard error when $n$ is large relative to population.

The sampling distribution is normal. Normal population always produces normal sampling distribution.

Variability of a statistic across different samples. Natural variation in statistics from sample to sample.

Allows approximation of sample mean distribution as normal. Enables normal approximation for inference procedures.

Sample must be random and representative. Random sampling eliminates systematic bias.

Distribution of a statistic over many samples. Shows how a statistic varies across repeated sampling.

Sample size $n$ is less than 10% of the population. 10% rule prevents finite population effects.

As sample size increases, standard error decreases. Standard error is inversely proportional to $\sqrt{n}$.

To allow normal approximation for sample means. Enables statistical inference about population means.

Larger sample size increases accuracy. Larger samples reduce sampling error.