Advanced Bonus Question 1 (5 points) When we do hypothesis t…

Advanced Bonus Question 1 (5 points) When we do hypothesis tests, First, we need to define our null hypothesis. Second, we need to assume the distribution of test statistics under the null hypothesis. For example, the z-test assumes normal distributions under the null hypothesis the t-test assumes t-distributions under the null hypothesis the F-test assumes F-distribution under the null hypothesis Third, we draw the null distribution and decide on critical value (CV) and rejection region based on the statistical significance level. Fourth, we get test statistics from observed sample data. Fifth, we need to compare test statistics with critical value (CV)  to decide whether to accept or reject the null hypothesis, or we need to compare p-value with statistical significance to decide whether to accept or reject the null hypothesis.  In particular,  when we know that (1) a random variable X in a population follows a normal distribution, (2) mean of X in the population  (3) randomly selected sample data for X from the population that follows a normal distribution. (4) sample mean and variance of X in the sample data.  However, we do not know ______________________ In this case, we can apply t-test for hypothesis tests.