Help with null hypothesis It has been claimed that at U.C.L.A. at least 40% of the students live on campus. From a sample of 250 students, 90 live on campus. Does the evidence support this claim at a = 0.01 . What i did is Ho: P is greater or equal to 0.4 Ha: P is less than 0.4 The critical value comes out to be -2.33 from the table Now how to calculate the test statistics? Also is my critical value correct?

Think of them as a sample of iid variables whose values are either zero or one and $\mu=p$. Recall then that your test statistic, as always when testing for the mean with iid data, takes the form

$$\sqrt{n} \frac{\bar x - 0.4}{\hat\sigma},$$

where $\hat\sigma$ is the sample standard deviation which, in this very special case, you can replace with the known population standard deviation under $H_0$ if you wish. Just plug in the numbers and you're done.

And yes, you looked it up correctly.