Psych 7: Sample Means

Ch. 7

12 cards   |   Total Attempts: 182
  

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Define the distribution of sample means (sampling distribution)
The collection of sample means for all the possible random samples of a particular sample size (n) that can be obtained from a population
What are the characteristics of the standard error of the mean?
  1. As sample size increases, standard error of the mean will decrease
  2. The larger the population standard deviation, the larger the standard error of the mean
What is the primary purpose of a distribution of sample means?
To find the probability associated with any sample mean
What are the characteristics of a sample distribution (distribution of sample means)?
  1. Sample means should accumulate around the population mean
  2. Distribution of sample means will be normal (or close to normal) regardless of the same of the original distribution
  3. As sample size increases, sample means will more closely resemble the population mean
Explain these characteristics:
  1. Sample means should accumulate around the population mean
  2. Distribution of sample means will be normal (or close to normal) regardless of the shape of the original distribution
  3. As sample size increases, sample means will more closely resemble the population mean
  1. A sample should be representative of the population; in fact, samples tend fall within two standard deviations of a population, and when calculating sample standard deviation, we even need to adjust to capture a wider variability that is descriptive of the population.
  2. Most samples have a mean that's representative of population mean, and therefore extreme scores on either end will be unlikely.
  3. The larger the sample size, the lower the standard error of the mean, meaning the variability between sample means and the population mean will be smaller.
What is the relationship between sampling error and the distribution of sample means?
The smaller the sampling error, the less deviation there will be between the scores on a sampling distribution (the more compact the distribution will be).
Define central limit theorem
The distribution of sample means will approach normal as the sample size approaches infinity (with n = 30, the distribution of sample means is almost perfectly normal).
Define the standard error of the mean
The amount of distance, on average, expected between a sample mean and a population mean
How is the standard error of the mean similar and dissimilar to standard deviation?
  1. They both measure variability
  2. Std. error of the mean measures the variability of sample means, where as std. deviation measures the variability of individual scores in a distribution
What are similarities and differences between standard deviation and the standard error of the mean?
  1. Similarities: both measure variability using mean as a reference point
  2. Differences: standard deviation measures raw scores while standard error of the mean measures sample means
How do each of the following affect or change the value of the standard error of the mean?
  1. The population standard deviation
  2. The sample size
  3. The population mean
  1. The larger the population standard deviation, the larger the standard error of the mean
  2. As sample size increases, standard error of the mean will decrease.
Describe the similarities and differences between the sampling distributions of n = 12 and n = 100
  1. Similarities: they both accumulate around the population mean
  2. Differences: n = 12 will be slightly negatively skewed, while n = 100 will be normally distributed; furthermore, the standard error of the mean will be greater for n = 12 than for n = 100.