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CI and Hypothesis Test

What is the relationship between a confidence interval and a single sample, two-tailed hypothesis test?

How are they the same? How are they different?

Review the definition of a single sample, two tailed test. Now review the structure of a confidence interval.

What are the assumptions and requirements for the use of each?

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Confidence intervals and two-tailed tests are very similar. They answer similar questions and have similar calculations.

Hypothesis tests and confidence intervals:

When you do a one-sample two-tailed test, you are testing the following hypotheses:

Null hypothesis: the mean is equal to 0 (μ = 0)
Alternative hypothesis: the mean is different than 0 (μ ≠ 0)

(I put these examples in terms of testing means, but you might also be testing proportions, standard deviations, or any other population parameter. You could also compare the parameter to any number, not just 0.)

Once you do the test, you will reject the null hypothesis if there is sufficient evidence. "Sufficient" usually means that the test returns a p-value of 0.05. Therefore, if you get a p-value of less than 0.05, you will reject the null hypothesis. (You can also use different significance levels; 0.10, 0.05, and 0.01 are the most popular.)

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