PSYC 220 - Psychological Statistics: Sampling Distribution & Central Limit Theorem

These flashcards cover key concepts related to sampling distribution and the Central Limit Theorem from the PSYC 220 lecture on Psychological Statistics.

What does the Central Limit Theorem (CLT) state about the sampling distribution when the population distribution is normal?

If the population distribution of X is normal, then the sampling distribution of the sample means is also normal.

What is the shape of the sampling distribution as sample size increases, according to the CLT?

The sampling distribution approaches a normal distribution when the sample size n is large (n ≥ 30).

In a normal distribution with a mean of μ=30 and a standard deviation of σ=2, what is the probability of selecting a big dog with a weight of ≥32 lbs?

Calculate the Z-score and use the standard normal distribution table to find the probability.

Define empirical distribution.

Empirical distribution shows all possible values of a variable (e.g., weight) collected from the population.

What is a theoretical distribution?

A theoretical distribution describes the expected probabilities of a variable based on known parameters, like a normal distribution defined by its mean and standard deviation.

What is meant by the term 'sampling error'?

Sampling error refers to the difference between the sample mean and the population mean due to randomness in sample selection.

How do you obtain the empirical distribution of the sample means?

By taking repeated random samples of a specified size from the population and calculating the sample mean for each sample.

What is the fundamental problem of statistics when comparing a sample to a population?

We often want to infer results about the population mean from a sample mean, which introduces uncertainty.

What formula is used to calculate the Z-score for sample means?

Z = (X̄ - μ) / (σ/√n), where X̄ is the sample mean, μ is the population mean, and σ is the population standard deviation.

What is the standard deviation of the sampling distribution also known as?

The standard error.