Miller - Chapter 5 - Hypothesis Testing - Study Notes - Page 92 Typos #4

[Dr. Jayanthi Sankaran]

Hi David,

As referenced above, Question #4:

4) A sample of 25 money market funds shows an average return of 3.0% with standard deviation also of 3.0%. Your colleague Peter conducted a significance test of the following alternative hypothesis: the true (population) average return of such funds is GREATER THAN the risk-free rate (Rf ). He concludes that he can reject the null hypothesis with a confidence of 83.64% .i.e., there is a 16.36% chance (p value) that the true return is less than or equal to the risk-free rate. What is the risk-free rate (Rf ). (note: this requires look-up calculation)

Answer is d) 2.40%

The one-tailed t-stat that is associated with 16.36% with 24 degrees of freedom is 1.059 and not 1.00.
eg.TINV(16.36%,24) = - 1.4309 and not -1.00. Standard error of sample mean = 3.0%/SQRT(25) = 0.60%. Since t stat = 1.059 and not 1.00, (.03 -Rf )/0.60% = 1.059, such at Rf = 3.0% - 0.64% = 2.36% and not 2.40%. Although, this may be trivial, just wanted to point it out - I guess you have approximated it to 1.0 and -1.0 to make it simpler, because as degrees of freedom increases, the t distribution tends to a standard normal!

Thanks!
Jayanthi

 

[ShaktiRathore]

Yes Jayanthi
As sample size<30 we should use t distribution instead of normal. I think David has used approximated value rounded to 1 place of decimal. Using exact value of 1.059 instead of 1 approx. One,(.03-Rf)=.6%*1.059= .6354% or Rf=3-.6354%=2.3646%~2.365~2.37~2.4% what David got, u got the answer rounded to 2 places of decimal as 2.36%. Yes answer can be given rounded to any place of decimal,if rounded to places answer is 2.37% but if rounded to 1 place answer is 2.4%. Also taking 1 makes calculation easier.
Thanks

 

[Dr. Jayanthi Sankaran]

Thanks, for confirming Shakti - appreciate it!

Jayanthi