# Qua Qua QUA!

Two independent samples are taken and their statistics calculated as follows: Population 1: Sample size 12, mean 325 and standard deviation 40 Population 2: Sample size 12, mean 288 and standard deviation 44 A researcher hopes to demonstrate that the mean of population 2 is less than the mean of population 1 to a 95% level of significance. What is the critical t-value assuming that the two population variances are equal?

dont have my quant book on me booourns!

you asking for the reliability factor?

however independant samples= pooled variance

I am asking to find the t-critical…I think in this one is a bit tricky

strange you are not asking for us to memorize that crazy @\$\$ formula are you!

Nope dont worry!

a terrible formula gives a 23.78 as degrees of freedom, which is t critical 1.714 (for 23)

map1 Wrote: ------------------------------------------------------- > a terrible formula gives a 23.78 as degrees of > freedom, which is t critical 1.714 (for 23) and what formula is that. I am looking for it in book – it is definitely not in SECRET SAUCE

Result: The hypothesis test performed is a one-tailed test. The two samples are less than 30, which means that the differences in means will be t-distributed with n1 + n2 - 2 degrees of freedom i.e. df = 22. For an alpha of 0.05 the t-tables, for 22 df give us a critical value of 1.7171.

strangedays Wrote: ------------------------------------------------------- > Result: > > The hypothesis test performed is a one-tailed > test. The two samples are less than 30, which > means that the differences in means will be > t-distributed with n1 + n2 - 2 degrees of freedom > i.e. df = 22. For an alpha of 0.05 the t-tables, > for 22 df give us a critical value of 1.7171. so you always do a one tailed test when N is < 30 ??? is that the takeaway ?

daj224 Wrote: ------------------------------------------------------- > strangedays Wrote: > -------------------------------------------------- > ----- > > Result: > > > > The hypothesis test performed is a one-tailed > > test. The two samples are less than 30, which > > means that the differences in means will be > > t-distributed with n1 + n2 - 2 degrees of > freedom > > i.e. df = 22. For an alpha of 0.05 the > t-tables, > > for 22 df give us a critical value of 1.7171. > > > so you always do a one tailed test when N is < 30 > ??? is that the takeaway ? Man I dunno…I also got this question wrong… and I hoped someone here could explain it…so we are on the same boat

it is one-tailed because you are testing a greater than or less than hypothesis if it were =30, it would be a two tailed

strangedays Wrote: ------------------------------------------------------- > A researcher hopes to demonstrate that the mean of > population 2 is less than the mean of population 1 > to a 95% level of significance. What is the > critical t-value assuming that the two population > variances are equal? --------------------------------------------------- in Q, researcher would like to find out if X2=X1. in hypothesis 0, = must be included. so H0:X2>=X1 Ha:X2

page 475 volume 1 CFAI text

map1 Wrote: ------------------------------------------------------- > page 475 volume 1 CFAI text ------------------------------------------------------ in the sample of page 475 volume 1 CFAI text, they are asking if mean return in 80s different than mean return in 70s. i.e. X1=X2 or X1=/X2 . it is 2-tailor test. in this Q, researcher want to know if mean of population 2 is less than the mean of population 1 . it is one-tailor test. but the t-value calculation is same no matter one or two tailor test.