ajb1 wrote:
@tickersu I’m clearly not following you. Are you saying the answer is #3 “above the upper confidence band”
I believe so– it doesn’t appear to require knowledge beyond how to interpret significance based on a CI (in this case, control limits). The question:
From Wiley: When using quality control charts, the null hypothesis that the manager has no skill should be rejected when the manager’s performance at the end of the relevant period is:
1. above the lower edge of the confidence band.
2. between the lower confidence band and the upper confidence band.
3. above the upper confidence band
…
Ho: Manager has no skill
Ha: Manager has skill (performance ABOVE some threshold for significance)
When do we reject Ho?
As with any CI, a result is not significant on a two-tailed test when the hypothesized (null) value falls within the confidence interval (period value outside the control limits, for this case). In a one-tailed test (could be implied here, because skill is associated with increased returns, in this case, so positive tail outcomes), a hypothesized value is not significant (do not reject) when the hypothesized value (period value) is below the upper band of the CI (control chart).
Answer choice 2 says between the bands—not significant, fail to reject Ho.
Answer choice 1 says
above the
lower edge of the CI (or lower control limit)—> in other words, it is not a lower value than the lower band, so it can’t be significant on a two-tailed test.
If the test of hypothesis is only one-tailed, then you have a significant result only in scenario 3 where the sample statistic exceeds the upper control limit.
No matter which way you set up the test, one or two-tailed, there is only one solution here that implies statistical significance (performance beyond the control limit).
…
Their answer:
Answer is #1. The confidence band represents a range of values that could be due to random luck rather than skill, and as such we would not reject the null hypothesis that the manager has no skill if the returns lie in this range
…
Their reasoning supports my conclusion. They’re telling you why #2 is incorrect (by implying do not reject), but they’ve neglected that choice #1 is included in choice #2.
Unless I’m misunderstanding something here…(I haven’t seen the book, so it is possible, but I’m not quite sure that’s the case.) Maybe someone can ask S2000 his thoughts.
Read up on statistical control charts (beyond the finance context) for more background…anything outside the control limits implies that the process is no longer in control (think of manufacturing and a machine needs to be serviced, causing too many defects from an out of control process). In that case, the null is that the process is in control, and the null is rejected when certain patterns appear on the chart or a value exceeds one of the bands.
Additionally, the explanation isn’t the most accurate. Even values that are beyond the confidence bands could be due to sampling variation (random luck), but these values have just exceeded our threshold for deciding what was due to sampling error and what indicates evidence against the null (hence, we call them significant, but it’s not guaranteed they weren’t due to sampling variation [“manager’s luck”]).