P1.T2.70 - Standard error Page 101 - #70.4

[Dr. Jayanthi Sankaran]

Hi David,

In #70.4 - Assume we know the population of hedge fund returns is normal with mean of 8% but population volatility is unknown. What is the probability that the sample mean return (n = 40 is sample size) will exceed 10%, if the sample volatility is 10%?

(a) 10.0%
(b) 10.3%
(c) 10.7%
(d) 11.1%

Answer C (10.7%)

The t statistic is 1.26 and the degrees of freedom are 39. And P(t > 1.26) with 39 df is given by T.DIST.RG(1.26, 39) = 10.7%
However, given that we don't have access to Excel, if we use the T-table, Pr(t>1.2658, 39) falls between Pr(t>0.681) = 0.25 and Pr(t>1.303) = 1.10. and so Pr(0.681<=1.2658<=1.303 = 0.25 - 0.10 = .15 = 15%
How can arrive at the exact answer of 10.7%?

Thanks
Jayanthi

 

[ShaktiRathore]

Hi jayanthi,
We need to find x such that 1.303x+(1-x).681=1.2658=>.622x=.5848=>x=.94
Pr(t>1.2658)~.94*.10+.06*.25=.094+.015=.109=10.9% closer to actual answer .i hv taken weighted avg of area in terms of how far or close actual t value 1.2658 is from critical values. In general in such way u can find for any t stat whose table value is not given i think it gives good approximate answes
Rs.
Thanks

 

[Dr. Jayanthi Sankaran]

Hi Shakti,

Thanks - I was also thinking of doing linear interpolation, but was not sure whether we could do so. In Corporate Finance for NPV calculations, linear interpolation is common for computing discount rates. And so, I presumed that one could do the same for these Statistical tables, too - although I was not 100% sure!

Thanks for confirming
Jayanthi

 

[Dr. Jayanthi Sankaran]

Incidentally, I did get my copy of the Fourth edition of Gujarati. At the time, you took your FRM exam, you were so lucky that Gujarati was the prescribed text. For those of us, like myself, preparing for the May 2015 FRM - Part I, we are subject to a pell-mell of Miller! Wonder why GARP does this?

Thanks
Jayanthi