Quick questions on Hypothesis testing: hypotheses, significance levels and critical regions - OCR A-Level Maths A

The critical region is the set of outcomes so extreme that you reject $H_0$. You either compare the probability of the observed result (or more extreme) with the significance level, or find the critical region first and check whether the observation falls in it.

For bivariate data you can test whether there is genuine correlation in the population. The hypotheses are $H_0: \rho = 0$ (no correlation) against a one- or two-tailed alternative, and you compare the sample correlation coefficient $r$ with a critical value from tables for the sample size and significance level.

For a two-tailed test at the $5\%$ level, what probability sits in each tail? [1 mark]

A sample of $25$ from $N(\mu, 9)$ has mean $\bar{x}$. State the standard deviation of $\bar{X}$. [2 marks]