Probability & Statistics

If two events $A$ and $B$ are independent, which equation holds?

A researcher has a sample mean from $n=25$ with unknown population variance. Which test is most appropriate to test a mean vs a known value?

Which distribution is most appropriate for modeling the number of rare events in a fixed interval when events occur independently?

In linear regression, which interpretation of the slope coefficient is correct?

A study reports $p=0.03$ for a two-sided test at $\alpha=0.05$. Which is the best interpretation?

Which practice most directly increases the risk of overfitting in regression?

For a symmetric distribution, the mean and median are equal.

A $95\%$ confidence interval means there is a $95\%$ probability that the parameter lies in the computed interval for the observed data.

Failing to check residuals in regression may hide violations like nonlinearity or heteroscedasticity.

Explain how to decide between using a $t$-test and a $z$-test for a sample mean and mention one common inference mistake when using these tests.

Match each test/method with its typical use: