Section A

You must answer ONE question, using a separate document for the question
(weighting is 50%). Word limit is noted against each sub question. Equations are
excluded from your word limit. Anything you write beyond the word limit will not be
marked.

QUESTION 1

A researcher runs an experiment to measure the impact of a short nap on memory. There
are 200 participants and they can take a short nap of either 60 minutes or 75 minutes. After
waking up, each participant takes a short test for short-term recall. Each participant is
randomly assigned one of the examination times, based on the flip of a coin.

Consider the following regression model:

𝑠𝑐𝑜𝑟𝑒𝑖 = 𝛾0 + 𝛾1𝑛𝑎𝑝𝑖 + 𝑢𝑖 (1)

where 𝑠𝑐𝑜𝑟𝑒𝑖 is the test score by the student 𝑖, 𝑛𝑎𝑝𝑖 is the amount of time for which the
student slept prior to taking the test (𝑛𝑎𝑝𝑖 = 60 or 75) and 𝑢𝑖 is the error term.

(a) Explain what the term 𝑢𝑖 represents. Why will different students have different values of
𝑢𝑖? [Maximum 150 words]

(b) With reference to relevant OLS assumption(s), explain if the OLS estimators (𝛾̂0, 𝛾̂1) are
unbiased. [Maximum 350 words]

(c) The researcher wants to test if that nap has no effect on test score at 1% significance
level. Write down and explain all Stata codes required for this hypothesis test including
the appropriate critical value. No calculation is needed. [Maximum 100 words]

(d) Suppose 𝑢𝑖|𝑛𝑎𝑝 ~𝑁(0, 𝜎2). Explain the factors that affect the variance of 𝛾̂1. How can
this variance be estimated? [Maximum 200 words]
(Total 50%)