Statistical Inferences PDF
Document Details
Uploaded by ExceedingChrysoprase7632
Monash University
Tags
Summary
This document discusses the relationship between confidence intervals (CI) and hypothesis tests. It provides an example to illustrate how a 95% CI can be used to determine if a population parameter has changed. The document also notes the difference between one-sided and two-sided tests.
Full Transcript
Statistical Inferences Relationship between CI and Test of Significance Relationship between CI and Test of Significance 2 One and two-sided tests and CIs Note how confidence interval and hypothesis test complement each other…but are not...
Statistical Inferences Relationship between CI and Test of Significance Relationship between CI and Test of Significance 2 One and two-sided tests and CIs Note how confidence interval and hypothesis test complement each other…but are not entirely equivalent when it is a one-sided test. Example: Average height of certain population is known to be 171cm. Has this changed? Let’s assume: 95% CI based on data is (171.17,174.61). Since 171 is outside CI, we can, 95% confident, claim difference. Two-sided test at α=0.05. Test statistic will be large in magnitude, in particular 2.24, yielding p-value range (0.02, 0.04). Since p-value range is smaller than α, we reject H0 and conclude that data gives statistically significant evidence for difference stated in Ha. CI are inherently two-sided…so 95% CI and the test based on α=0.05 will have same conclusion only if the test is two-sided. Consider 1-sided p-value of 0.025
