An investment manager advertises that he beats the Russell 2000 by 3% per year. An analyst looks at the last 20 years and finds a performance rate of 2.8% over the Russell 2000 with a standard deviation of .9%.
And another one: On the basis of a sample, an analyst tests the hypothesis that the mean current ratio of companies that file for bankruptcy within two years is 0.5 or less.
Anybody cares to formulate H0 and Ha?
for the first one: If you want to show that the advertisement is not true, then: H0: p=>3 % HA: p<3 % Remember: what u want to show, is HA
First is equality, null mean=3%, alternative not equal Second is inequality, null mean<=0.5, alternative >0.5
Hey map, why to test equality in the first? To beat an index sounds one tailed… cfaisok
ye, but it is “beat by 3%”
Yeah he says he will beat by three percent. To beat by 3 % means (in an advertisement) to outperform by at least 3 %. You are right, you could read it like you have written. But a quant-analyst would test this one tailed. I mean: why should we test the hypothesis? To show that the advertising is misleading. No investor is really interested if he get 3 % versus 3.000001 %. So it is clearly two tailed.
So it is clearly two tailed. ups: one tailed
Both 1-tail…
So, what is the claim? that the manager beats the index by 3% (i read this as "exactly 3%, not more, not less). I’m only interested if this is true or false, not by how much down or above.
map, but look… Assume the real population mean is 3.0001. And now we take a big sample and your test would (hopefully) reject H0. And now what’s your conlusion. the manager makes a wrong statement !? --> that why the test is one tailed.
To tell you the truth, map, theoretically you are right. But this is an exam for practioners…
Second one: On the basis of a sample, an analyst tests the hypothesis that the mean current ratio of companies that file for bankruptcy within two years is 0.5 or less. Ho: p>0.5 Ha: p<= 0.5 I read it as he wants to prove that companies filing bankruptcy is 2 years or less is 0.5 current ratio. Isn’t that the Ha ?
H0 ALWAYS involves some form of equality. Ha NEVER involves equality.
Map1 is correct. First is two-tailed, and the second is one-tailed per answer provided.
map1 Wrote: ------------------------------------------------------- > H0 ALWAYS involves some form of equality. Ha NEVER > involves equality. and do you know why? Because you cannot prove equality. You can only reject it.
I would prefer to be dead wrong in the first, and have the manager beat the index by more than 3%
dreary from which database do have this stuff?
cfaisok, > No investor is really interested if he get 3 % versus 3.000001 %. So it is clearly two tailed. right, but then why did you set your Ha: u < 3?