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10 Cards in this Set
- Front
- Back
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Statistical Inference
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methods for drawing conclusions about a population from sample data.
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Margin of Error (aka Standard Error):
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shows how accurate we believe our guess is based on the
variability of the estimate of x . Unfortunately named, the margin or standard error is the standard deviation of the sample! Calculated by ( ) ˆ(1 ˆ) ˆ x p p SE p n σ − = = or more easily ( ˆ ) ˆ ˆ x SE p pq n |
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Conditions for Construction of a Confidence Interval for μ
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a level C confidence interval, calculated from data usually in the form
estimate ±margin of error which gives the probability that the interval will capture the true parameter value in repeated samples. C represents the percentage of confidence . ˆ ˆ CI x z* pq n |
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Confidence Interval:
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a level C confidence interval, calculated from data usually in the form
estimate ±margin of error which gives the probability that the interval will capture the true parameter value in repeated samples. C represents the percentage of confidence . ˆ ˆ CI x z* pq n |
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Critical Value z*:
Behaviors |
a chosen z-score such that the central area under the normal curve between
–z* and +z* will capture the desired percentage of confidence C. Most common values for z* are 1.645 for a 90% confidence interval 1.960 for a 95% confidence interval 2.576 for a 99% confidence interval 1. Smaller margins of error create smaller levels of confidence. 2. To cut the margin of error in half, you must take four times as many observations. |
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Sample Size for Desired Margin of Error
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Solve the following for n:
ˆ ˆ z* pq m n ≤ , where m is the desired margin of error |
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Significance Test:
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assess the evidence provided by data about some claim concerning a population.
Simply put: an outcome that would rarely happen if a claim were true is good evidence that the claim is not true. Assess the strength of the evidence against the null hypothesis. |
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Null hypothesis
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the statement being tested in a significance test. Usually phrased as “no effect”
of “no change” symbol 0 H . |
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Alternative hypothesis
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the claim about the population that one is trying to find evidence for.
Symbol a H . |
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Types of Tests
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One Sided, Two sided
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