Practice exam, 2023
Each question is worth 33 points and the exam is out of 99 points. Complete all
3 questions. You should complete the exam within 2 hours. No outside sources
can be used on the exam, but you can refer to the t/z tables posted on moodle.
LSE approved calculators are allowed.
1. True or false: please indicate whether a statement is true or false and provide
a brief (up to 3 sentences for each part) justification for your answer.
a. (3 points) A simple random sample of 10,000 Americans will not be
able to provide you with useful information about political
preferences in the entire US because the sample is too small.
b. (3 points) If you calculate a 95% confidence interval for a population
mean, you have established a range within which 95% of sample
means will be.
c. (3 points) Choosing a significance level of 1% is always better than
choosing a significance level of 5%.
d. (6 points) Experiments will always yield smaller estimated causal
effects than non-experimental comparisons because experiments
account for reverse causality and omitted variables bias.
e. (6 points) Suppose you run a regression with a very large dataset.
Your stata output tells you that your estimated coefficient on the
explanatory variable of interest is 3 and the t-stat reported in the stata
output is 3. You are able to conclude that the estimated slope is
statistically significantly different from 1 at alpha equals 0.05.
f. (6 points) If you compare the slope estimate for an explanatory
variable in a simple regression with the slope estimate for the same
explanatory variable in a multiple regression, the slopes will be
different.
g. (6 points) If you compare the slope estimate for an explanatory
variable in a simple regression with the slope estimate for the same
explanatory variable in a multiple regression, and the sign flips, then
you should focus on the simple regression due to collinearity.
2. Suppose you have been hired by a law firm to test for wage discrimination by
gender at a leading consulting firm. You are provided with salary data on 174
employees of the consulting firm, and estimate a regression model predicting
salary using experience working in the firm, a gender dummy variable (male
= 1; female = 0), and the interaction of the two.
The regression output looks like the following:
a. (5 points) Specify the two regression lines estimated here: one for men
and one for women.
b. (4 points) Are women’s earnings ever predicted to exceed men’s If so, at
what level of experience
c. (4 points) A colleague looks at the regression output above and says,
“These data don’t make sense – they suggest that additional experience
lowers men’s wages.” Evaluate the employee – is s/he doing a good job
by engaging with the data and making sure it is tied to reality
d. (10 points) A colleague looks at the following scatterplot and says, “this is
clearly evidence that the firm does not discriminate against women.”
Come up with a reasonable argument along this colleague’s lines.
e. (10 points) Another colleague looks at the same scatterplot (above) and
says, “this is clearly evidence that the firm does discriminate against
women.” Come up with a reasonable argument along this colleague’s
lines.
3. A/B tests are online experiments in which individuals arriving at a website
are randomly shown one of two versions (A or B). These are powerful tools
for firms to learn how to optimize their websites to maximize revenues.
Suppose you run a hipster shoe company selling expensive sneakers. You
decide to conduct an A/B test on your website. Some individuals who visit
your company’s website are randomly shown a short video with a celebrity
endorsement of the product, while others are just presented with the site as
usual. You need to decide whether the increased sales generated by the video
justifies the use of these endorsement videos in the future as a general sales
strategy.
a. (3 points) Suppose sales are greater among individuals who view the
endorsement video than among individuals viewing the standard
website. Was this likely due to omitted variables bias or to reverse
causality
b. (5 points) Suppose sales are greater among individuals who view the
endorsement video. Is it definitely the case that in the future sales will
be greater if endorsement videos are generally adopted Provide two
reasons why this may not be the case.
c. (5 points) Suppose you conduct a comparison of means test and find
that the sales level among individuals who view the endorsement
video is statistically significantly greater than the sales level among
individuals who visited the standard website. Does this imply that you
should adopt the endorsement video
d. (10 points) Suppose your sales team tells you that the video will be
profitable if the proportion of individuals who view the endorsement
video who purchase a product is greater than 50%. Suppose you’re
A/B test included 100 customers who viewed the endorsement video
and that 60% of them purchased the product. Under what condition
do you adopt the endorsement video strategy
e. (10 points) If you establish an action threshold based on alpha equals
0.05, what is the power of your test to reject the null hypothesis if the
true proportion of individuals who view the endorsement video who
purchase a product is 55%
