type I and II error

[happyking02]

Suppose that all of a firm’s managers are outperforming the benchmark, some by a little, some by a lot. If the confidence intervals for a quality control charts in portfolio management were widened, what would the most likely effect be?
A) Type I error would become more likely and Type II error would become more likely.
B) Type I error would become less likely and Type II error would become more likely.
C) Type I error would become more likely and Type II error would become less likely.
Can u please explain? thanks!

 

[kevinf12]

I think it is B. As increasing the desired confidence level = widening intervals (if you picture the charts it should mean the bands around the mean are more spaced out…if that makes sense).
So, if the bands are larger it is more likely that people’s returns will fall within them. That is, if it falls within (speaking towards the illustrations in CFA text) the bands it indicates you cant reject the null, meaning you cant attribute the performance to skill. So there would be more likelihood you would say that a manager’s performance is NOT due to skill and potentially fire/not hire a manager who does actually outperform based on skill.

 

[Captain Barbosa]

B is correct
if you widen the chart you will wrongly reject the managers that are significantly different from zero. So VA>0 and do not reject null hypothesis is box 4 type II error

 

[bidder]

B is correct for sure
The area between the confidence bands represent Ho.
The areas above and below the confidence bands represent Ha.
So by widening the confidence bands, the Ho area will be larger, thus there is a higher chance you will not reject Ho when in fact Ho is incorrect. This is the same as saying there is a higher chance that you will commit a Type II Error.
By widening the confidence bands, the Ha areas will less likely be crossed, thus there is a lower chance you will not reject Ho when in fact Ha is correct. This is the same as saying there is a lower chance that you will commit a Type I Error.

 

[Boris_7]

Type I is reject more (than should be). Type II is reject less.
Widen the band, we reject less. So it is B.

 

[happyking02]

bidder Wrote:
——————————————————-
> B is correct for sure
>
> The area between the confidence bands represent
> Ho.
> The areas above and below the confidence bands
> represent Ha.
>
> So by widening the confidence bands, the Ho area
> will be larger, thus there is a higher chance you
> will not reject Ho when in fact Ho is incorrect.
> This is the same as saying there is a higher
> chance that you will commit a Type II Error.
>
> By widening the confidence bands, the Ha areas
> will less likely be crossed, thus there is a lower
> chance you will not reject Ho when in fact Ha is
> correct. This is the same as saying there is a
> lower chance that you will commit a Type I Error.
thanks. This explanation really helps.

 

[kevinf12]

Also, just another small point, but if you get a multiple choice and have no clue, you can at least eliminate one if they have type I and type II move in the same direction…

 

[lenchik101]

Remember that Type I is keeping a bad manager
Type II is firing a good manager
The wider your confidence interval (you are including a higher percentage of value-added outcomes for a given manager), the more likely that more of your manager’s possible value-added returns will lie within the confidence band (which reduces your likelihood of keeping a zero value added manager - reducing Type I). This means you are not keeping zero value added managers. but at the same time, you are increasing your chances of firing a true value added manager, because according to your confidence interval, his returns will fall within this wider interval even though they could be trully value added. thus you are increasing your Type II error of firing managers that are value added.

 

[1morelevel]

This is not L3 material correct?

 

[LaGrandeFinale]

very much L3

 

[bidder]

HappyKing02 - you’re welcome!
Have a look at the graphic, visualise it, then forget the words. You will be able to recraft the words in the exam if you can visualise what I described. It’s in the CFAI curriculum.
Cheers.