Determine whether the following inference form is valid or invalid. MC 4.2b Question 7.png

Let X be a discrete random variable representing the number of times a student’s laptop will die during college (i.e., how many new laptops they’ll need to buy). X=0 means their original laptop never dies, and X=4 means they have four laptops die. It is also possible to observe X=1, X=2, or X=3, but no other values. The probability distribution is given byP(X=m) = (4-m)/10.What is the mean of X?

You have a cross-sectional dataset from 2014 with one observation per country.  The Y variable is annual GDP growth (%), and the X variable is a measure of democracy, where 1=most democratic and 0=least democratic.  You are interested in the slope coefficient in the linear projection of Y onto (1,X), i.e., the parameter b in LP(Y | 1,X) = a + bX.  You’ve heard rumors that the less-democratic countries sometimes intentionally report GDP growth that is better than reality, but you have no way to actually test that hypothesis because in your dataset you only observe the GDP growth reported by each country, not the true GDP growth (unless they are identical).  Let Y* be the true annual GDP growth, Y the observed/reported value, and  M = Y – Y*  the measurement error.  If the rumor is true, then the OLS slope estimator has _______ asymptotic bias.  (Hint: draw a picture.)

The following graph shows one component of a decomposed time series (Johnson & Johnson’s earnings per share); which component does it most look like?

Let Y be hourly wage, D=1 if female (and D=0 otherwise), and X=age. You want to estimate the CMF of log wage, E[ln(Y) | D=d, X=x]. One reason the true CMF is probably not linear-in-variables is

Descriptively, you’re curious about the difference in college attendance rates between students who take at least one “advanced placement” (AP) class in high school (X=1) vs. students who never take any AP class (X=0).  You have data on “number of AP classes taken” for every single student who graduated from high school in Missouri in Spring 2020.  You also have data from every single college/university in Missouri on every student enrolled for Fall 2020.  For each student in your first dataset, you assign X=0 or X=1 depending on the number of AP classes, and then you generate Y=1 if they appear in your Fall 2020 enrollment dataset or else Y=0. Consider two points:A.  your first dataset excludes students who should have graduated from high school in Spring 2020 but dropped out (i.e., will not even graduate high school); they all should have Y=0 and (almost all) X=0, but instead they do not appear in your sample.B.  the very best Missouri high school students (who all have X=1) often attend college in other states (like Stanford in CA, Harvard in MA, etc.), so they are incorrectly coded as Y=0. For your estimator of the mean difference E(Y|X=1) – E(Y|X=0), point A causes _____ bias, and point B causes ____ bias.

Assume that the true causal effect of a 3rd-grade child in Kenya having an insecticide-treated bed net (ITN; to prevent mosquito bites, to reduce incidence of malaria) is attending 10 more days of school per year than with no bed net. If we take a random (iid) sample of children in Kenya who just completed 3rd grade, and we subtract the average school attendance (in days) of children with no bed net from the average attendance of children with an insecticide-treated bed net, the expected value of this difference (in days) is

You have the time series data Yt of your company’s sales (in millions of dollars) in each year t.  You want to model the sales growth rate.  You should model

Descriptively, you’re curious about the difference in college attendance rates between students who take at least one “advanced placement” (AP) class in high school (X=1) vs. students who never take any AP class (X=0).  You have data on “number of AP classes taken” for every single student who graduated from high school in Missouri in Spring 2020.  You also have data from every single college/university in Missouri on every student enrolled for Fall 2020.  For each student in your first dataset, you assign X=0 or X=1 depending on the number of AP classes, and then you generate Y=1 if they appear in your Fall 2020 enrollment dataset or else Y=0. Consider two potential problems:A.  your first dataset excludes students who should have graduated from high school in Spring 2020 but dropped out (i.e., will not even graduate high school); they all should have Y=0 and (almost all) X=0, but instead they do not appear in your sample.B.  the very best Missouri high school students (who all have X=1) often attend college in other states (like Stanford in CA, Harvard in MA, etc.), so they are incorrectly coded as Y=0. These are best categorized as

Let W=1 if a household has more than zero children (under age 18), and W=0 otherwise.  Let Z be the number of children in the household.  Conditional on a household having a non-zero number of children, the probability of having (exactly) two children is