(First interview) Assuming the population is normally distributed, answer each statement true or false. (a) When viewed as a random variable, the sample mean follows a normal distribution. (b) The population mean is always equal to the population median. (c) The sample mean is always equal to the sample median. (d) The MLE of the population standard deviation is unbiased.

(First interview) A colleague says that a 95% confidence interval has a 95% probability of containing the true population mean of height. Is he right?

(First interview) Answer the statements true/false. (a) The law of large numbers says that as the sample size increases the distribution of the sample mean will become closer to the normal distribution. (b) When performing simple univariate linear regression, the slope of the regression line after regressing X on Y is always the same as the slope of the regression line after regression Y on X. (c) If a father whose height is far above average has a son whose height is barely above average, this can be explained by the regression effect. (d) The distribution of the sample standard deviation follows the t-distribution with the number of degrees of freedom equal to the sample size minus one.

(Second interview) Tell me in your own words, pretending that your audience is a non-statistician, what is simple linear regression (or simple univariate regression) and what might you use it for? (a) What are the assumptions or conditions that need to be met to use this model? (b) What is the mathematical model that we are trying to fit? (c) Let’s say you have a bunch of data, like (x, y) pairs. Mathematically, how do you actually fit the model? How do you transform those x’s and y’s into a slope and intercept? (d) Let’s say that you have some data, you check all the assumptions and conditions, and everything looks good except there doesn’t seem to be normality. Can you still use the model? Or can you use parts of it and not others?

(Second interview) In the context of hypothesis testing, what are type 1 and type 2 errors?

(Second interview) What is a p-value? (a) Mathematically, how do you compute it? (b) Some journals have banned reporting p-values in articles they’ve published. Can you describe what a reasonable person’s objections might be to using p-values? (c) If you were going to present results without a p-value, what other statistical tool would you use to communicate the same thing?

(Second interview) You have a trial for a drug to lower blood pressure. The treatment group gets the new drug, control gets the old drug. Conduct experiment under optimal conditions, p-value is really really tiny. Can we conclude the old drug is more effective than the old drug?

(Second interview) Suppose you have a fair 12-sided die. How many times on average you have to roll this die before seeing the first 3