Question

“Assuming the null hypothesis is true, the expected value of every test statistic we have seen this semester, whether it is a z, t, or chi-square test statistic, is 0.”
One of your friends says the above statement.
Respond to this statement.
In your response, include,
1) For z tests about population proportions: what is the distribution and the corresponding expected value of a z test statistic under the null.
2) For t tests about population means: what is the distribution and the corresponding expected value of a t test statistic under the null.
3) For chi-square tests about categorical models: what is the distribution and the corresponding expected value of the chi-square test statistic under the null.

Answer 1

Assuming the null hypothesis is true, the expected value of every test statistic we have seen this semester, whether it is az, t, or chi-square test statistic, is 0."

1) For z tests about population proportions:

This is not always case, in one-way ANOVA, the expected value of F- test statistics when H0 is true is
E(F) = 1