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# confidence intervals watch

1. hello

i am having a bit of trouble with this question
i have attached the question. please could u have a look at the question

my answer: control limits (3.05, 135)
is that correct?

Attached Images

2. (sum from i = 1 to 5) (X(i) - Xbar)^2 ~ 10 chi^2(4)

[chi^2(4) is the chi-squared distribution with 4 degrees of freedom]

From statistical tables,

P(chi^2(4) <= 0.2971) = 0.01
P(chi^2(4) >= 13.28) = 0.99

So the control limits are 10*0.2971 = 2.971 and 10*13.28 = 132.8.

--

If the actual stable variance is v then the probability of a false alarm (ie, the probability of an alarm when the process is stable) is

P(v*chi^2(4) <= 2.971 or v*chi^2(4) >= 132.8)
= F(2.971/v) + 1 - F(132.8/v)

where F is the CDF of chi^2(4). The attached graph shows that

- if v is more than 10 then the probability of a false alarm is more than 0.02,
- if v is less than 10, but more than about 7, then the probability of a false alarm is less than 0.02.
Attached Images

3. thanks for your help Jonny

u seem to always help me
but i still can't rep u again - so i'll just say thanks

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Updated: January 31, 2006
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