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Questions and Answers
What does a confidence interval (CI) indicate when testing the average height of a population known to be 171cm?
What does a confidence interval (CI) indicate when testing the average height of a population known to be 171cm?
In a one-sided hypothesis test, how does the confidence interval differ from a two-sided test?
In a one-sided hypothesis test, how does the confidence interval differ from a two-sided test?
What should be concluded if the 95% CI for a population mean is (171.17, 174.61) and the known mean is 171cm?
What should be concluded if the 95% CI for a population mean is (171.17, 174.61) and the known mean is 171cm?
What is the primary relationship between the confidence interval and the hypothesis test at α=0.05?
What is the primary relationship between the confidence interval and the hypothesis test at α=0.05?
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What is implied if the p-value range for a hypothesis test is (0.02, 0.04) at α=0.05?
What is implied if the p-value range for a hypothesis test is (0.02, 0.04) at α=0.05?
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For a one-sided test with a p-value of 0.025, what does this suggest about the null hypothesis?
For a one-sided test with a p-value of 0.025, what does this suggest about the null hypothesis?
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Study Notes
Relationship Between Confidence Intervals and Tests of Significance
- Confidence intervals (CIs) and tests of significance are complementary statistical tools that help us draw inferences about population parameters from sample data.
- While they are closely related, they are not entirely equivalent when dealing with one-sided tests.
One and Two-Sided Tests and CIs
- Consider an example where we want to determine if the average height of a certain population has changed from a known value of 171 centimeters.
- If the 95% CI based on the sample data is (171.17, 174.61), we can be 95% confident that the average height has changed because the known value of 171 centimeters falls outside the confidence interval.
- A two-sided hypothesis test with alpha = 0.05 would lead to the same conclusion, as the p-value would be less than alpha, indicating statistically significant evidence for a difference.
- However, if the hypothesis test was one-sided, the conclusions might differ.
- In the provided example, the one-sided p-value is 0.025, which is less than alpha, suggesting a statistically significant difference for a one-sided test.
- However, this does not align with the confidence interval's conclusion.
- This discrepancy arises because CIs are inherently two-sided, while one-sided tests focus on a specific direction of change.
- Therefore, a 95% CI and a two-sided test with alpha = 0.05 will yield the same conclusion only if the test is also two-sided.
- This is because a 95% CI represents a range that captures 95% of the possible values of the population parameter, while a two-sided test investigates departures from the null hypothesis in both directions.
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Description
Explore the relationship between confidence intervals and tests of significance in statistics. Understand how they complement each other and the implications of one-sided versus two-sided tests in hypothesis testing. This quiz will help you master these essential statistical concepts.
