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Describe the connection between confidence intervals and hypothesis testing, in particular for single sample T tests.

Describe the connection between confidence intervals and hypothesis testing, in particular for single sample T tests.

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Answer #1

We know that the confidence interval for the population mean when we do not given the value for the population standard deviation is related to the two-tailed one-sample t-test. For example, 95% confidence interval for the population mean is related to the 5% significant test for population mean. We cannot use the confidence interval for the one tailed tests such as lower tailed or upper tailed tests.

If we reject the null hypothesis of two-tailed t-test, then claimed population mean should not contain in the confidence interval.

If the claimed population mean is not present in the confidence interval, then we can reject the null hypothesis for the two tailed t test for the single sample t test.

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