Satistics

Greenwich University
Asef Khan
BSc Economics : Estimation And Hypothesis Testing
Tutor: Alexander Guschanski
06/03/2023 9-11am

MODULE ASSESSMENT
General points
 Some emailed re group allocation he has replied to all.
 Any issues please speak to him
 Hope you have started on assessment- don’t leave it to the end


Feedback
 Students did online feedback via Mentimeter.
 Thanks to those who took part- positive feedback. Not able to vote on first question
because of technical issue but voted on second- apologies for wrong settings
 Speak to personal tutors if you have specific issue to discuss
 Pace of the lecture- the majority thought too fast- so will slow down the pace/keep
at similar level; level of difficulty was ok for most though some said too difficult and
too fast and not enough explanation on the slide
 KEY- lecture for you is not to learn the material;you will not be able to absorb it
during the lecture. Point of lecture is to introduce the material and enable you to
ask questions.
 Preferably you should have completed prep before the lecture- lecture slides are not
substitutes for a textbook. That Is Not The Goal. Lectures are a compliment to
textbook reading
 He wants to leave one whole session for revision of the material for the exams- in
that session he won’t introduce any new material and will send out a Google doc in
advance where you can suggest material/exercises you would like to go over. He will
also discuss online exam- you’ll have an opportunity to practice that too
 Suggestion from students that labs and tutorials are two hours not one- that is not
possible right now
 The idea of the module is to focus in the library studying and working with
colleagues
 Thanks for the feedback- continue talking to him re difficulties during office hours
etc
 Also feel free to use comments and questions- see Padlet where you can comment
anonymously
TODAY’S LECTURE
 Cover estimator basics + hypothesis testing- both are the culmination of all we
have learnt so far




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, Greenwich University
Asef Khan
BSc Economics : Estimation And Hypothesis Testing
Tutor: Alexander Guschanski
06/03/2023 9-11am

Confidence intervals- what was special about the way we estimated them last week in
comparison to week before?
o Last week –created confidence intervals purely based on info that we
obtained from the sample where we don’t know whole pop-( e.g., how big)
or distribution
o We took sample from the distribution and based on mean and variant from
sample we could construct a confidence interval for the mean of the
population
o We needed to account for the additional uncertainty re not knowing the
population or variant- so needed to use student T distribution
PART 3 ESTIMATOR BASICS-TOUCHED ON BRIEFLY LAST WEEK
 Taking step back, interested in estimation of population mean -what did we use to
get an estimate of this? Which stat? What do we use from the sample to get an idea
of the mean of the population? e.g. average income UK is 100 random citizens-
what’s the best guess of mean of population?
o Use the mean of the sample as that is best guess( don’t use the standard
deviation)
o How to calculate mean of sample= add up income of people and divide by
100(n)=best guess( theta hat)
 Best guess because the sample mean is unbiased. The expected value of the stat is
equal to the population parameter=theta hat.Population parameter = mean average
income of population
 Theta hat- is a guess- estimator for the population parameter BUT why take an
expected value ?
o Because if you take a different sample you will get different sample means –
BUT expected value of sample mean is still population parameter
 See graph- distribution of sample mean is equivalent to blue distribution. Why
does it have distribution? Every time you take sample , get different mean( different
points on horizontal axis) but on average you are landing at population parameter
 Sufficient repeated examples> but average of those sample means will be the
population parameter or population average
Biased estimators- graph
 Green area=biased estimator; biased because taking different samples would mean
locating estimator to right of population and so over- estimating the population
parameter average
 Graph- expected value of second estimator ( yellow distribution theta 2 hat)- bias is
the difference between expected value of the second estimator and true
population parameter

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