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Chapter 7: Probability and Samples: The Distribution of Sample Means -…
Chapter 7: Probability and Samples: The Distribution of Sample Means
Population = entire group of scores.
Sample = subset of a population.
Parameter = numerical value describing a population.
Statistic = numerical value describing a sample.
Random sampling gives every individual an equal chance of selection.
Sampling error occurs because samples differ from populations.
Sample means vary from one sample to another.
Distribution of sample means = collection of means from all possible samples.
The mean of the distribution of sample means equals the population mean.
Symbol for population mean = μ.
Symbol for sample mean = M.
Expected value of M = μ.
Standard Error abbreviation = SE.
Formula for standard error: SE= σ/ sqrt of n
Standard error measures variability among sample means.
Larger sample sizes produce smaller standard errors.
Smaller standard errors create more precise estimates.
Sampling distribution approaches normality as n increases.
Central Limit Theorem (CLT) explains this normality.
CLT applies regardless of population shape when n is sufficiently large.
Sample means are less variable than individual scores.
Z-scores can be used with sampling distributions.
Formula for z-score of a sample mean:
z= (M-μ)/σM
Probability can be calculated using z-scores.
Researchers use sampling distributions to evaluate unusual outcomes.
Most sample means cluster near μ.
Extreme sample means occur less frequently.
Sampling distributions form the foundation for hypothesis testing.