Standard Error

The Standard Error of M provides a measure of how _________________, on average, a sample mean represents its corresponding population mean

Accurately

Because the distribution of sample means tends to be normal, what does this allow you to do in terms of probabilities?

Because the distribution of sample means tends to be normal, the z-score value obtained for a sample mean can be used with the unit normal table to obtain probabilities

How does standard error describe the distribution of sample means

By describing the variability in the distribution of sample means

Although if two (or more) samples are selected from the same population, they probably have different means, you should expect the sample means selected to be...

Close to the population mean

The distribution of sample means has well defined and predictable characteristics that are specified in

The Central Limit Theorem

The Central Limit Theorem states that the mean of the distribution of sample means is called __________________

The Expected Value of M

According to the Central Limit Theorem the standard deviation of the distribution means is called _____________

The Standard Error of M

How is the distribution of sample means defined?

The distribution of sample means is defined as the set of means from all the possible random samples of a specific size (n) selected from a specific population

What is the expected value of M

The mean of the distribution of the sample of means is equal to the mean of the population of scores (μ)

What is the Standard Error also known as?

The standard deviation of the distribution of sample means

The procedure for computing z-scores and finding probabilities for sample means vs the procedure used for computing z-scores and finding probabilities for individual scores

They are essentially the same procedure

What is the goal of Research?

To show that what you found is dissimilar from that of which you would find regularly

According to the Central Limit Theorem The Expected Value of M is always equal to

The population mean μ

The Standard Error of M is defined as

The standard deviation of the distribution of sample means

The standard error provides a measure of

The average distance between the sample mean (M) and the population mean (μ)

The shape of the distribution of sample means tends to be

Normal

Standard Error describes the

Distribution of sample means

Notation for Standard Error of M?

σM

How is the Standard Error of M calculated for samples?

σM = σ _____ √n

How is the Standard Error of M calculated for populations?

σM= σ₂ _____ n

Rules of z-scores for locating sample means in a distribution of sample means (3)

1. A positive z-score indicates a sample mean that is greater than the population mean (μ) 2. Negative z-score corresponds to a sample mean that is smaller than (μ) 3. The numerical value of the z-score indicates the distance between the sample mean (M) and the population mean (μ) measured in terms of the standard error

Law of Large Numbers (3)

1. Law for Standard Error 2. The larger the sample size (n), the more probable that the sample mean (M) is close to the population mean (μ) 3. Inverse relationship: the larger the sample size, the smaller the standard error

There are aspects of the _______________ that may not be included within a _____________

1. Population 2. Sample

What is sampling error? (2)

1. The error between a sample statistic and the corresponding population parameter 2. The measure of of discrepancy between the sample and the population

The shape of the distribution of sample means is guaranteed to be normal if either (2)

1. The population from which the samples are obtained is normal 2. Or The sample size is n= 30 or more

Within the distribution of sample means, the location of each sample mean can be specified by

A z-score

What is the z-score formula for finding the location of each sample mean in a distribution of sample means by using a

M - μ z = ───── σM

If two (or more) samples are selected from the same population, the two samples will probably have different ____________

Means

______________ provide an incomplete picture of the population

Samples

The standard error of M measures the

Standard distance between a sample mean and the population mean

What is different from the way you compute probabilities when using sample means compared to when you use individual scores?

When you are using sample means you must remember to consider the sample size (n) and compute the standard error (σM) before you start any other computations

What is also important to remember regarding the distribution of sample means before using the unit normal table?

You must be sure that the distribution of sample means satisfies at least one of the criteria for normal shape before you can use the unit normal table