Chapter 7 Flashcards
Law of large numbers
The larget the sample size (n) in a specific sample, the more probable that M is close to mu (larger sample, smaller standard deviation)
Standard error of the mean
(OM)
- 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)
Distribution of sample means
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
Central Limit theorem
- Mean of the theoretical distribution of sample means is called the Expected value of M (always equal to the population mean)
- 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)
- The shape of the distribution of sample means is typically normal
- Distribution of sample means approaches a normal distribution as n approaches infinity
When is the distribution of sample means guaranteed to be almost perfectly normal?
- 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
Z-Test for distribution of sample means
- 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)
What is the standard error of M?
The standard deviation of the distribution of sample means
Sampling error
The natural discrepancy, or amount of error, between a sample statistic and its’ corresponding population parameter
Distribution of Sample Means
- 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
Sampling distribution
A distribution of statistics obtained by selecting all the possible samples of a specific size from a population
Characteristics of Distribution of Sampling Means
- 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.
Central Limit Theorem (Textbook)
- 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
- DOSM has mean = to population mean (mu)
- DOSM has a standard deviation of (o/square root of m)… standard error of the mean
- DOSM will approach a normal distribution as n approaches infinity (by the time n=30)
The expected value of M
- The mean of the distribution of sample means is equal to the mean of the population of scores (mu)
The Standard Error of M
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
