I am not sure if I am understanding this correctly. Was hoping if someone may assist in regards to T-test.

My question is when do we use “Confidence Intervals” comparred to using merely “Critical Value for the test statistic” to reject H0. The reason why I am asking is because I seen both of the examples above used as rejection basis.

You construct a confidence interval when you’re estimating the value for a population parameter; e.g., based on my sample of 500 giraffes, there’s a 90% chance that the average height of all giraffes in the world is between 5.4m and 5.6m. You use critical values for a statistic (t, F, z, χ-square, whatever) to establish the limits on the confidence interval.

You also use critical values for a statistic (t, F, z, χ-square, whatever) to establish the limits on the acceptance region for hypothesis testing. In that sense, hypothesis testing is nearly identical to confidence intervals.

The former is the t-calc for confidence intervals for a single observation; say, next month’s bond return.

The latter is _ very _ specialized: it’s the t-calc for whether r (the correlation coefficient) is zero. You use it only for correlation coefficients, not for general data (such as monthly returns).