MATH 2565 - Lecture 11

Toward Statistical Inference & Sample Means (Ch 5.1-5.2)

A number that describes a population is called a

Parameter

A number that describes a sample is called a

Statistic

What is Population Distribution?

The distribution of values for all members of the population

What is Sample Distribution?

The distribution of values inside one single sample of size n

What is Sampling Distribution?

The distribution of a statistic (like ¯ x) across all possible samples of the same size from the population

Why Samples?

Less time-consuming

Less costly

Less cumbersome

A good sampling scheme, must have both low ____ and low _____.

Bias, Variability

What should we use to reduce bias and to reduce variability respectively?

Random Sampling and a Larger Sample

If the population X has mean µ, then x̅ has ______.

mean µ

When we take the mean of all possible sample means, it will equal to the ____________ ______ regardless of sample size n

population mean

The standard deviation of sample mean is also referred to as

Standard Error (SE) of the sample mean

As the sample size increases, the sampling distribution becomes more ________ around the true population parameter

centered

What will happen to the sampling distribution of the sample mean if the sample size is large enough?

The distribution will be approximately normally distributed

The C² Rule: To reduce the standard deviation by a factor of C, we must increase the sample size by a factor of

C²

For the Central Limit Theorem (CLT), what value must n be equal or greater than for the sampling distribution of the sample mean x̅ to be approximately normal?

30

What will be the shape of the sampling distribution of X̅:

C