To construct a confidence interval using the given confidenc

To construct a confidence interval using the given confidence level, do whichever of the following is appropriate, Find the critical value z alpha/2, find the critical value t alpha/2, or state that neither the normal nor the t distribution applies. 99%; n = 100; sigma = 19.0; population appears to be skewed Choose the correct answer below. t alpha/2 = 2.626 t alpha/2 = 1.984 z alpha/2 = 2.575 z alpha/2 = 1.96 Neither the normal nor the t distribution applies.

Solution

We can use the Central Limit Theorem when the number of observations is greater than 40. Next, because we know the value of the standard deviation, we can use the z-score. In this case alpha is 1-.99=.01, so alpha/2=.005. This corresponds to a z value of 2.576. Here is a diagram that tells when to use which test statistic: http://bloomingtontutors.com/blog/when-to-use-the-z-test-versus-t-test

Hope this helps!