Quant - Confidence Interval Question

When you are constructing a CI and you have your T-Stat +/- T(critical)*(SE)

When do you just use the T-critcal value from the book and not multiply it by the SE?

One of the questions on the Schweser practice exam has it just being the critical value.

For constructing a confidence interval, you _ always _ multiply the t-critical value by the standard error.

Can you paraphrase the question (or, rather, the answer) in which they said that you wouldn’t?

" Hara is correct to fail to reject the null hypothesis that the value of the slope coefficient is equal to 4.0 at the 5% level of significance.

The critical t-value for the slope coefficient with 31 − 2 = 29 df at the 5% level for a two-tailed test is 2.045. The test statistic is (2.897 − 4.000)/0.615 = −1.79. The absolute value (1.79) is less than 2.045, and the correct decision is to fail to reject the null hypothesis that the slope coefficient is equal to 4.0."

That’s what I suspected: you’re not building a confidence interval; you’re testing an hypothesis.

When testing an hypothesis, you have two approaches:

  • Use the calculated test statistic as-is, and build an acceptance region using the hypothesized mean, the critical values, and the standard error.
  • Normalize the test statistic (subtract the hypothesized mean, then divide by the standard error), and build an acceptance region using only the critical values.

They did the latter. What you describe as the test statistic is, in fact, the _ normalized _ test statistic; the test statistic is 2.897.

Thank you. So they won’t explicitly say when you normalize or is it when you are not testing significance ie not equal to 0?

You’re welcome.

As I wrote above, you can use either approach with equal effectiveness; use whichever one appeals to you.