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Z-test and Confidence Intervals
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Z-tests when the standard deviation is known, confidence intervals using Z and T distributions, critical values & regions, type Ⅰ vs ⅠⅠ errors.
Want a deeper conceptual understanding? Try our interactive lesson!
Normal confidence interval using technology
AHL AI 4.16
Your calculator should include a statistical test called Zinterval or similar. To use it:
Enter the value of σ, which must be known for a Z-test of any kind.
Enter either
Data: a list of values you've typed into the calculator
Stats: the sample mean xˉ and n, the number of samples.
Enter the confidence level and hit calculate
The calculator returns the desired interval, which is symmetrical around xˉ.
T-interval confidence interval using technology
AHL AI 4.16
Your calculator should include a statistical test called Tinterval or similar. To use it:
Enter either
Data: a list of values you've typed into the calculator
Stats: the sample mean xˉ, the sample standard deviation Sx and n, the number of samples.
Enter the confidence level and hit calculate
The calculator returns the desired interval, which is symmetrical around xˉ.
Z-Test for population mean
AHL AI 4.18
Z-tests allow us to test the mean of a sample against
a population with known mean: use Z-Test
another sample: use 2-SampZTest
a paired sample: calculate the difference, then use Z-Test with μ0=0.
Critical values & regions
AHL AI 4.18
When testing the mean of a sample against a population, the critical region is the set of values for the sample mean that would lead to rejecting the null hypothesis. The critical value(s) is (are) the boundary of the critical region. In other words, the critical value is the threshold for xˉ that leads to a p value exactly equal to the chosen significance level.
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