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Definition
| mathematical techniques that allow us to make decisions, estimates, or predictions about a larger group of individuals (a population) based on the data collected from a much smaller group (a sample) |
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| represents the number of standard deviations away from the mean a score falls |
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| distribution of sample mens (DSM) |
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| shows the means of many samples drawn from one particular population |
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Definition
| when a distribution of sample means is created from large samples (N greater than or equal to 30), the DSM will resemble a normal distribution regardless of whether the samples were drawn from a population that was distributed normally or non-normally |
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| single-sample formal test of hypothesis |
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Definition
| provides the mean of a particular population (mu) and the mean of a sample (x-bar) and the test will allow us to decide whether the sample could have been drawn from the known population or if the sample must have been drawn from a different population |
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| the population for which we are told mu |
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| population from which the sample was drawn |
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| we do not know, until the end of the problem, whether the sample comes from the known population or from a different population, so we refer to it as this before / during testing |
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| the hypothesis that statistical tools can demonstrate is highly unlikely (can disprove); contradicts the Ha; taking into account every other possibility than the one the researcher is hoping to demonstrate true |
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| what the researcher wants to demonstrate is true (differs from status quo) |
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| if we suspect that mu for the population from which the sample was drawn will be less than or greater than the known population mean then our hypothesis is directional (lower-tailed, or upper-tailed) |
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| non-directional hypotheses |
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Definition
| if we can't predict whether mu for the population from which the sample was drawn will be less than or greater than the known population mean, but we believe it will be different than the known population we state that mu does not equal a particular value (two tailed) |
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Definition
| an area on the DSM for the known population that represents where the sample mean must fall before we will reject the null hypothesis |
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Definition
| the value set before conducting a statistical test that indicates how rare a sample must be before we will decide that it does not come from the known population |
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| states that the population from which the sample was drawn has a mean higher than the known population |
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| states that the population from which the sample was drawn has a mean lower than the known population |
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| states that the population from which the sample was drawn has mean different than the known population |
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| critical value (Lesson 5) |
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Definition
| a z- or t- score we get from a probability table that indicates how far the sample mean (x-bar) must be from the mean of the DSM (mu sub x-bar) before the sample is considered very rare; indicates the boundary of the rejection region |
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Definition
| much like the z-distribution (mound-shaped, symmetrical, with a mean of 0) but it is wider--reflecting the higher variability of sample means for smaller sample sizes |
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| decision rules (lesson 5) |
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| state in words what has to be true for us to reject the null hypothesis -- what has to be true for our sample mean to fall in the rejection region |
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| calculated value (lesson 5) |
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Definition
| the z-or t-score for the sample mean we were given; it is obtained by using a formula; it indcates how far the sample mean (x-bar) actually is from the mean of the DSM (mu sub x-bar) |
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| conditions that must be met in order for our hypothesis-testing conclusion to be valid |
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| Standard Deviation of a Distribution of Sample Means |
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Definition
| the researcher concludes -- on the basis of the sample data they have -- that there really is a difference between populations, when in truth there is no difference between the populations (the sample comes from the known population) |
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Definition
| the researcher concludes -- on the basis of the sample data they have -- that there is no difference between populations, when in truth there is a difference between the populations ( the sample comes from a population other than the known population) |
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| the "sensitivity" of the test -- it is the probability that a statistical test will lead to a decision to reject the H0 when H0 is indeed false |
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Definition
| the exact probability of obtaining, from the known population, a sample as rare or more rare than the one we were given |
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| descriptive statistics calculated for sample data; the sample mean (x-bar) is an example |
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Definition
| descriptive statistics calculated for data from an entire population; the population mean (mu) is an example |
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| a single number that represents a population parameter |
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| a range of values around a sample statistic that estimates a population parameter |
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Definition
| estimates the mean of a population (mu) from which the sample was drawn by calculating a range of values around the sample mean (x-bar) that is highly likely to include the mean of the entire population (mu) -- with 0.90, 0.95, 0.99 |
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| for each CI you calculate, will be expressed as a percentage: 90%, 95%, 99% |
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| the probability that the CI encloses the population mean. Depending on the confidence level, the confidence coefficient might be 0.90, 0.95, 0.99 |
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| the probability that the confidence interval does not enclose the population mean (1 - confidence coefficient) |
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| critical values (lesson 7) |
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Definition
| z-scores or t-scores that are upper and lower boundaries of the confidence interval |
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Definition
| provides a narrow range of values into which we believe the population mean will fall |
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| an estimate with a high confidence level |
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