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In: Statistics and Probability

What is the relationship between hypothesis testing and statistical prediction intervals? How does the p-value serve...

What is the relationship between hypothesis testing and statistical prediction intervals? How does the p-value serve as importance in this relationship?

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Expert Solution

A confidence interval is an range of values which likely to contain a unknown population parameters.

A hypothesis is nothing but the assumption which we have to test based on the sample data.

Confidence intervals and hypothesis tests are similar in that they are both inferential methods that rely on an approximated sampling distribution. Confidence intervals use data from a sample to estimate a population parameter. Hypothesis tests use data from a sample to test a specified hypothesis.

P value is the minimum level of significance.

You can use either P values or confidence intervals to determine whether your results are statistically significant. If a hypothesis test produces both, these results will agree.

  • If the P value is less than your significance (alpha) level, the hypothesis test is statistically significant.
  • If the confidence interval does not contain the null hypothesis value, the results are statistically significant.
  • If the P value is less than alpha, the confidence interval will not contain the null hypothesis value.

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