Explain carefully the relationship between a confidence interval, a one-sided hypothesis test, and a two-sided hypothesis test. What is the unit of measurement of the t-statistic?

What will be an ideal response?

Answer: In the case of a two-sided hypothesis test, the relationship between the t-statistic and the confidence interval is straightforward. The t-statistic calculates the distance between the estimate and the hypothesized value in standard deviations. If the distance is larger than 1.96 (size of the test: 5%), then the distance is large enough to reject the null hypothesis. The confidence interval adds and subtracts 1.96 standard deviations in this case, and asks whether or not the hypothesized value is contained within the confidence interval. Hence the two concepts resemble the two sides of a coin. They are simply different ways to look at the same problem. In the case of the one-sided test, the relationship is more complex. Since you are looking at a one-sided alternative, it does not really make sense to construct a confidence interval. However, the confidence interval results in the same conclusion as the t-test if the critical value from the standard normal distribution is appropriately adjusted, e.g. to 10% rather than 5%. The unit of measurement of the t-statistic is standard deviations.