1. ## Class boundaries-Frustrating

The durations (in minutes) of 100 phone calls were recorded, resulting in the frequency distribution below.

duration of calls 0- 1- 2- 3- 4- 5- 10- >20
Frequency 7 18 34 25 13 2 1 0.

Does this mean to the nearest minute and so the class boundaries would be 0<= min <0.5, 0.5<=min<1.5 etc

or 0<=min<1,1<=min<2, 2<=min<3 etc. The question is for testing goodness of fit.

Also

Y is distributed as N(50,100). One hundred observations of Y result in the following frequency distribution. Carry out a goodness of fit test at the 2.5% sig level.

observations of Y <30 30- 40- 50- 60- >70
Frequency 3 14 30 35 14 4

I dont know what the real boundaries should be??
29.5>Y, 29.5<=Y<39.5, etc

or something else.

Thanks!

2. It's a little hard to tell from your table, but I am guessing that there is no rounding going on. The table could be written as
$\displaystyle \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline 0-$1^{-}$& 1-$2^{-}$& 2-$3^{-}$& 3-$4^{-}$& 4-$5^{-}$& 5-$10^{-}$& 10-$20^{-}$&$\geq 20$\tabularnewline \hline 7 & 18 & 34 & 25 & 13 & 2 & 1 & 0\tabularnewline \hline \end{tabular}$

For the second part,

$\displaystyle \begin{tabular}{|c|c|c|c|c|c|} \hline$<30$& 30-$40^{-}$& 40-$50^{-}$& 50-$60^{-}$& 60-$70^{-}$&$\geq 70$\tabularnewline \hline 3 & 14 & 30 & 35 & 14 & 4\tabularnewline \hline \end{tabular}$

In the problems that I have seen they normally give you the boundaries. There is some ambiguity about which side of the boundary the equality lies. On the other hand, if these are continuous random variables, then it does not make any difference!