Chapter 7

Question 1

Law of large numbers

Answer 1

The larget the sample size (n) in a specific sample, the more probable that M is close to mu (larger sample, smaller standard deviation)

Question 2

Standard error of the mean

(OM)

Answer 2

• Provides a measurement of the average expected distance between the M and u (should remind you of standard deviation)
• Describes the distribution of sample means (variability)

Question 3

Distribution of sample means

Answer 3

the set of sample means for all possible random samples of a specific size (n) that can be selected from a population
-This distribution is has well-defined and predictable characteristics that are specified in the Central Limit Theorem

Question 4

Central Limit theorem

Answer 4

1. Mean of the theoretical distribution of sample means is called the Expected value of M (always equal to the population mean)
2. The standard deviation of the theoretical distribution of sample means is called the Standard error of M and is computed by oM (0/Square root of n)
3. The shape of the distribution of sample means is typically normal
4. Distribution of sample means approaches a normal distribution as n approaches infinity

Question 5

When is the distribution of sample means guaranteed to be almost perfectly normal?

Answer 5

• If the population the samples are obtained from is normal
• If n is 30 or greater

When n is greater than 30, the shape of the distribution is almost normal regardless of the shape of the original population

Question 6

Z-Test for distribution of sample means

Answer 6

• Z-test and unit normal table can be used for probabilites regarding the distribution of sample means because the distribution of sample means tends to be normal
• We use a slightly different z-score formula (swap standard error of m for standard deviation)

Question 7

What is the standard error of M?

Answer 7

The standard deviation of the distribution of sample means

Question 8

Sampling error

Answer 8

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

Question 9

Distribution of Sample Means

Answer 9

• The collection of sample means for all the possible random samples of particular size (n) that can be obtained from a population
• Is what the ability to predict sample characteristics is based on
• Contains all the possible samples (which is necessary to compute probabilities)
• now values are not scores but statistics (sample means)
• often called the sampling distribution of M

Question 10

Sampling distribution

Answer 10

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

Question 11

Characteristics of Distribution of Sampling Means

Answer 11

• Sample means should pile up around the population mean; most sample means should be relatively close to the population mean
• Pile of samples should tend to form a normal shaped distribution (frequencies should taper off as the distance between M and mu increases)
• The larger the sample size, the closer the sample means is to mu (more representative). Thus, the sample means obtained with a large sample size should cluster relatively close to the population mean; the means obtained from small samples should be more widely scattered.

Question 12

Central Limit Theorem (Textbook)

Answer 12

• Provides a precise description of the distribution that would be obtained if you selected every possible sample, calculated each sample mean, and constructed the distribution of the sample mean

1. DOSM has mean = to population mean (mu)
2. DOSM has a standard deviation of (o/square root of m)… standard error of the mean
3. DOSM will approach a normal distribution as n approaches infinity (by the time n=30)

Question 13

The expected value of M

Answer 13

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

Question 14

The Standard Error of M

Answer 14

The standard deviation for the distribution of sample means
1. Describes the distribution of sample means; provides a measure of how muchdifference is expected from one sample to another
2. Measures how well an individual sample mean represents the entire distribution

decreases when sample size increases (law of large #s)

When n=1 Om=O… whenever u are working w a sample mean u must use standard error