HBX CORE FINAL EXAM CORRECTLY
ANSWERED AND UPDATED.
A/B Test - CORRECT ANSWER 1) An experiment that compares the value of a dependent variable (ex =
likelihood that a website visitor purchases an item) across two different groups (control group and
treatment group). Members of each group must be RANDOMLY SELECTED to ensure that the only
difference between the groups is the "MANIPULATED" independent variable (ex = size of the font on
two otherwise identical websites)...a hypothesis test that tests whether the means of the dependent
variable are the same across the two groups; also used to test whether another parameter - ex =
standard deviation - is the same across two groups
Adjusted R-Squared - CORRECT ANSWER Measure of explanatory power of a regression analysis.
Adjusted R squared = R-squared*adjustment factor that decreases slightly as each independent variable
is added to regression model. Adjusted R-squared DROPS when a new independent variable is added
that does not improve the model's true explanatory power (vs. R-squared which never decreases when a
new independent variable is added to a regression model). Adjusted R-Squared should always be used
when comparing the explanatory power of regression models that have different numbers of
independent variables.
Alternative Hypothesis - CORRECT ANSWER Theory or claim we are trying to substantiate and stated as
OPPOSITE OF A NULL HYPOTHESIS. When data allow us to nullify the null hypothesis, we substantiate
the alternative hypothesis.
Asymmetric Distribution - CORRECT ANSWER Probability distribution that is not symmetric AROUND THE
MEAN
Average/Mean - CORRECT ANSWER For a distribution with discrete values, mean = values of all data
points in the set / number of data points
Base Case - CORRECT ANSWER Category of categorical variable for which a dummy variable is NOT
included in a regression model. A regression model with a categorical variable that has n categories
should have n-1 dummy variables. The coefficients of the dummy variables included in the regression
model are interpreted in relation to the base case. The analyst can select any category to be excluded
from the regression model; however, different base cases lead to different interpretations of the
dummy variables' coefficients. Ex: Suppose we are trying to determine the average difference in height
, between men and women in a sample, and suppose that on average men are 5 inches taller than
women in the sample. If we use Female as the base case then the coefficient for the dummy variable for
Male would be +5. If we use Male as the base case, the coefficient for the dummy variable for Female
would be -5.
Bias - CORRECT ANSWER Tendency of a measurement process to over or under-estimate the value of a
population parameter. Although a sample statistic will almost always differ from the population
parameter, for an unbiased sample, the difference will be random. For a biased sample, the statistic will
differ in a systematic way. Common reasons for bias include non-random sampling methods and non-
neutral question phrasing.
Biased Sample - CORRECT ANSWER Not representative of the population from which it is collected.
Sampling practices that can introduce bias include poorly phrased survey questions and non-random
sampling.
Bimodal distribution - CORRECT ANSWER Multi-modal distribution with two clearly discernable peaks.
Peaks may be of same height (equal frequency) or one peak may be the true MODE while the other has
a very high (but not the highest) frequency.
Bin - CORRECT ANSWER Range of values used to categorize data. In a histogram, observations are
divided into a set of non-overlapping bins, each corresponding to a range of values. Bins are constructed
to ensure that the histogram contains all observations in the data set. Height of bar corresponding to
the bin = number of observations in the data set that fall within that bin's range. Usually all bins in a
given histogram are the same width (i.e. the difference between the largest value and smallest value is
the same for each bin). In an Excel histogram, each bin is labeled by the value of the upper boundary of
the bin's range. Ex: With three bins (each width 1 and labeled 1, 2, and 3), the bin labeled 2 contains all
observations greater than 1 and LESS THAN OR EQUAL TO 2.
Binomial Distribution - CORRECT ANSWER A distribution of the possible successful outcomes in a given
number of trials, where there are only two possible outcomes for each trial, and each trial has the same
probability of success (e.g. flipping a coin). Ex: The binomial distribution for the number of "heads" that
result from flipping a coin 50 times specifies the probability for each possible outcome, from observing 0
"heads" to observing 50 "heads". The binomial distribution is used to create CONFIDENCE INTERVALS for
proportions.
Central Limit Theorem - CORRECT ANSWER If we take sufficiently large randomly-selected samples from
a population, the means of these samples will be normally distributed regardless of the shape of the
underlying population. (Underlying population must have a finite variance).
ANSWERED AND UPDATED.
A/B Test - CORRECT ANSWER 1) An experiment that compares the value of a dependent variable (ex =
likelihood that a website visitor purchases an item) across two different groups (control group and
treatment group). Members of each group must be RANDOMLY SELECTED to ensure that the only
difference between the groups is the "MANIPULATED" independent variable (ex = size of the font on
two otherwise identical websites)...a hypothesis test that tests whether the means of the dependent
variable are the same across the two groups; also used to test whether another parameter - ex =
standard deviation - is the same across two groups
Adjusted R-Squared - CORRECT ANSWER Measure of explanatory power of a regression analysis.
Adjusted R squared = R-squared*adjustment factor that decreases slightly as each independent variable
is added to regression model. Adjusted R-squared DROPS when a new independent variable is added
that does not improve the model's true explanatory power (vs. R-squared which never decreases when a
new independent variable is added to a regression model). Adjusted R-Squared should always be used
when comparing the explanatory power of regression models that have different numbers of
independent variables.
Alternative Hypothesis - CORRECT ANSWER Theory or claim we are trying to substantiate and stated as
OPPOSITE OF A NULL HYPOTHESIS. When data allow us to nullify the null hypothesis, we substantiate
the alternative hypothesis.
Asymmetric Distribution - CORRECT ANSWER Probability distribution that is not symmetric AROUND THE
MEAN
Average/Mean - CORRECT ANSWER For a distribution with discrete values, mean = values of all data
points in the set / number of data points
Base Case - CORRECT ANSWER Category of categorical variable for which a dummy variable is NOT
included in a regression model. A regression model with a categorical variable that has n categories
should have n-1 dummy variables. The coefficients of the dummy variables included in the regression
model are interpreted in relation to the base case. The analyst can select any category to be excluded
from the regression model; however, different base cases lead to different interpretations of the
dummy variables' coefficients. Ex: Suppose we are trying to determine the average difference in height
, between men and women in a sample, and suppose that on average men are 5 inches taller than
women in the sample. If we use Female as the base case then the coefficient for the dummy variable for
Male would be +5. If we use Male as the base case, the coefficient for the dummy variable for Female
would be -5.
Bias - CORRECT ANSWER Tendency of a measurement process to over or under-estimate the value of a
population parameter. Although a sample statistic will almost always differ from the population
parameter, for an unbiased sample, the difference will be random. For a biased sample, the statistic will
differ in a systematic way. Common reasons for bias include non-random sampling methods and non-
neutral question phrasing.
Biased Sample - CORRECT ANSWER Not representative of the population from which it is collected.
Sampling practices that can introduce bias include poorly phrased survey questions and non-random
sampling.
Bimodal distribution - CORRECT ANSWER Multi-modal distribution with two clearly discernable peaks.
Peaks may be of same height (equal frequency) or one peak may be the true MODE while the other has
a very high (but not the highest) frequency.
Bin - CORRECT ANSWER Range of values used to categorize data. In a histogram, observations are
divided into a set of non-overlapping bins, each corresponding to a range of values. Bins are constructed
to ensure that the histogram contains all observations in the data set. Height of bar corresponding to
the bin = number of observations in the data set that fall within that bin's range. Usually all bins in a
given histogram are the same width (i.e. the difference between the largest value and smallest value is
the same for each bin). In an Excel histogram, each bin is labeled by the value of the upper boundary of
the bin's range. Ex: With three bins (each width 1 and labeled 1, 2, and 3), the bin labeled 2 contains all
observations greater than 1 and LESS THAN OR EQUAL TO 2.
Binomial Distribution - CORRECT ANSWER A distribution of the possible successful outcomes in a given
number of trials, where there are only two possible outcomes for each trial, and each trial has the same
probability of success (e.g. flipping a coin). Ex: The binomial distribution for the number of "heads" that
result from flipping a coin 50 times specifies the probability for each possible outcome, from observing 0
"heads" to observing 50 "heads". The binomial distribution is used to create CONFIDENCE INTERVALS for
proportions.
Central Limit Theorem - CORRECT ANSWER If we take sufficiently large randomly-selected samples from
a population, the means of these samples will be normally distributed regardless of the shape of the
underlying population. (Underlying population must have a finite variance).
