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Probability and Samples: The Distribution of Sample Means, . - Coggle…
Probability and Samples: The Distribution of Sample Means
Samples, Populations, and the Distribution of Sample Means
Sampling error
is the natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter.
The Distribution of Sample Means
is the collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population.
A
sampling distribution
is a distribution of statistics obtained by selecting all the possible samples of a specific size from a population.
Characteristics of the Distribution of Sample Means
The sample means should pile up around the population mean.
The pile of sample means should tend to form a normal-shaped distribution.
The larger the sample size, the closer the sample means should be to the population mean.
Shape, Central Tendency, and Variability for the Distribution of Sample Means
Central Limit Theorem
: The sampling distribution of the mean will always be normally distributed, as long as the sample size is large enough.
The Shape of the Distribution of Sample Means
: Normal when...
The number of scores (n) in each sample is relatively large, around 30 or more.
The population from which the samples are selected is a normal distribution.
Expected Value of M
: Where the mean of the distribution of sample means is equal to the mean of the population of scores.
Standard Error of M
: The standard error provides a measure of how much distance is expected on average between a sample mean (M) and the population mean (μ).
Three Different Distributions
Original Population of Scores
- This population contains the scores for thousands or millions of individual people, and it has its own shape, mean, and standard deviation.
Sample Selected from the Population
- The sample consists of a small set of scores for people who have been selected to represent the entire population.
Distribution of Sample Means
- This is a theoretical distribution consisting of the sample means obtained from all the possible random samples of a specific size.
z-Scores and Probability for Sample Means
Identifies the location with a signed number, so...
z-score identifies the location with a signed number so that the sign tells whether the location is above (+) or below (−) the mean.
The number tells the distance between the location and the mean in terms of the number of standard deviations.
More about Standard Error...
The biggest differences between now and Chapters 5 & 6 are:
We are now using the distribution of sample means instead of a distribution of scores.
We are now using the standard error instead of the standard deviation.
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