In: Statistics and Probability
please describe with examples the relationship between confidence intervals and hypothesis testing.
Okay, so we can also reach the conclusion of a two-sided statistical test based on the confidence interval provided.
In a statistical test, we compare the null hypothesis with the alternative hypothesis. The null hypothesis is the statement of no effect and generally says that the population parameter (mean/proportion etc) is equal to some hypothetical value.
We just see whether the hypothetical population parameter value (like the hypothetical population mean value / hypothetical population proportion) value lies in the confidence interval or not to reach a conclusion about the statistical test.
For example, consider a hypothesis test in which we have to see whether the population proportion of boys in a college is greater than girls i.e. we test whether p=0.5 or not.
We construct a confidence interval and find that we are 95% confident that the population proportion is between (0.52,0.60). Since 0.5 does not lie in this confidence interval, we reject the null hypothesis in favor of the alternative hypothesis that p is not equal to 0.5.
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