Number of Simulations Needed - Wording

[sisiducky]

Could anyone explain this wording game for me?

1. (TIA review lesson) Want a 90% probability that the simulated value of E[X] will be within 0.15 of the true value

In solution it says P[|Diff| < 0.15] >= 0.9
Shouldn't it be 0.15*miu (miu is the true value)?

2. (TIA PE4 #34) Want to be at least 90% of estimating F(1250) correctly within 1%.

In solution it says P[|Diff| < 0.01F] >= 0.9
Shouldn't it be 0.01 (since it doesn't have "of ..." in the end)?

I know "within k% of expected value" is <k%E[X], but the two examples above simply don't make sense to me.

[Quick Slant]

1. You are correct. Dave goofed that up, as well as the regular lesson on topic.

[daaaave]

Suppose that you are trying to measure a 100 cm stick, and come up with a measurement of 102 cm. Is your measurement within 0.1 cm of the true value? No, you are off by 2 cm, which is more than 0.1 cm. Is your measurement accurate within 10%? Yes, you are off by 2%, which is less than 10%. The difference isn't whether or not we have "of ..." in the end, but rather whether we are talking about an absolute standard of error (such as 0.1 cm) or a percentage standard of error (such as 10%). The two examples that you quote are similar: the first is talking about an absolute standard of error of 0.15, and the "of" is simply saying what number you wish to compare to, while the second is talking about a percentage error, and so we want to be within k% of the true value.

Incidentally, the phrasing of the second example is identical to an old exam problem on this topic.

[Quick Slant]

I understand your point, but the question is somewhat ambiguous. If your intent was amounts, then it would be easier to understand if the criterion was not given as a percent. You outsmarted me!

Thanks for the clarification Dave. That answers a big riddle I had with topic.

[sisiducky]

Originally Posted by daaaave

an absolute standard of error (such as 0.1 cm) or a percentage standard of error (such as 10%)

% sign is the key... I like that. Thanks Dave!