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I'm studying for past exam and I'm actually stumped on what a particular question is asking me. I've thought about it for days and I actually just don't know what are they asking. Can anyone interpret the question?

It's part (ii)

" The Hobbits living in the Shire are not known for being very tall: while 97.5% of the population is taller than 60 cm, only 2.5% of the population exceeds 122 cm. The average height of the 144 guest who attended Bilbo’s birthday party is 95 cm, with sample standard deviation 19 cm. Assume for the population’s height a normal model with unknown mean μ and fixed variance $\sigma ^2$ .

i) Show that the normal distribution is a conjugate prior for the normal sampling model μ (assuming $\sigma^2$ fixed)

ii) Elicit prior parameters for the prior of point 1 (without considering the data on Bilbo’s party)."

normally for normal prior we just have some $\mu_0$ and $\sigma_0^2$. If we are not to consider the data how can we pick any particular values? there is footnote for part (ii) "You may can use the following equality $\Phi(-1.96)=0.025"$

Can anyone shed some light on what the question is actually asking in part (ii)? I can do part (i) but just cant get my head around what part (ii) is asking me to do as we cannot consider the actual data available.

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In part (ii) you can use the population information -- that is, the distribution of all hobbits living in the Shire -- but not information about the hobbits who attended Bilbo's party, to elicit your prior parameters. So your prior should be a normal distribution such that 2.5% of its mass falls below 60 cm and 2.5% falls above 122 cm. This is enough information to determine the parameters of the prior.

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  • $\begingroup$ thank you! so I should pick $\mu_0$=91cm and $1.96\cdot \sigma_0=31\implies \sigma_0=15.82$ i.e $\sigma_0^2=250.16$? $\endgroup$
    – user24907
    Commented Apr 17, 2018 at 19:26
  • $\begingroup$ @user24907 Looks good! $\endgroup$
    – grand_chat
    Commented Apr 17, 2018 at 21:28

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