Question

In: Statistics and Probability

please describe with examples the relationship between confidence intervals and hypothesis testing.

please describe with examples the relationship between confidence intervals and hypothesis testing.

Solutions

Expert Solution

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.

  • If the hypothesized population parameter value lies in the confidence interval, then we fail to reject the null hypothesis
  • If the hypothesized population parameter value does not lie in the confidence interval, then we reject the null hypothesis in favor of the alternative hypothesis.

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.

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!


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