Chapter 7: probability and Samples (The distribution of sample means)

In this chapter we introduce the distribution of sample means, which allows us to find the exact probability of obtaining a specific sample mean from a specific population.

Sampling Error

the natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter.

The Distribution of Sample Mean

the collection of samples of means for all the possible random samples of a particular size that can be obtained from a population.

A Sampling distribution

a distribution of statistics obtained by selecting all the possible samples of a specific size from a population.

Central Limit Theorem

it states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger — no matter what the shape of the population distribution.

the expected value of M.

The mean of the distribution of sample means is equal to the mean of the population of scores, µ and is called ________

Standard error of M

the standard deviation of the distribution of sample means. It provides a measure of how much distance is expected on average between sample mean and the population mean.

The law of large numbers

states that the larger the sample mean will be close to the population mean.

sample

* refers to a smaller, manageable version of a larger group.
* used in statistical testing
* should represent the population as a whole and not reflect any bias toward a specific attribute.

2 separate samples from the same population will probably differ in:

different individual

different score

different sample

Distribution of sample mean

are statistics, not single scores

Sampling distribution

a distribution of statistics obtained by selecting all the possible samples of a specific size from a population.

Central Limit Theorem

For any population with mean of µ and a standard deviation σ, the distribution of sample means for sample size n will approach a normal distribution with a mean of m and a standard deviation = 𝞼/√n, as n approaches infinity.

The distribution of sample

it means “approaches” a normal distribution by the time the size reaches n= 30.

the expected value of M

The mean of the distribution od sample means always is identical to the population mean. This mean value is what is called

The Standard Error of M The standard error saves the following two purposes:

1\. It describes the distribution of sample means.

2\. Standard error measures how well an individual sample mean represents the entire distribution