Confidence Interval Question

This topic has 4 replies, 3 voices, and was last updated 3 weeks, 1 day ago by Fausto Galetto.

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September 26, 2020 at 4:54 am #250168
Fausto Galetto
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In a book about Statistics and Minitab I found:
1. Confidence interval estimation is a technique to estimate a population parameter (such as population proportion) using sample data. The estimate is calculated for a given confidence level and is expressed as an interval. The higher the confidence level is, the less precise the interval estimate. See Montgomery and Runger (2011) for an excellent introduction to confidence interval estimation.
An application of this technique to Six Sigma is illustrated using Minitab® in…

And
1. 2. the upper bound is 0.492 gram for the standard deviation (given by the chi-square method). This means that 95% of the hamburgers have fat content with a standard deviation that is lower than 0.492 gram.
I think that statements like 1 and 2 are misleading.

Do some of the colleagues can make some comments?

Thanks

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September 26, 2020 at 9:02 am #250169

Stephen Smith
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At their heart, confidence intervals state that x-percent of confidence intervals will encompass the population parameter. The wider the net you cast, the more often you’ll observe the true value. This lack of specificity comes at the cost of defining what the population parameter is.

The second part is more complicated. I’m not sure how confidence intervals reconcile with asymmetric probability distributions. Since the chi-squared distribution exists in the domain of zero to positive infinity, the hard, lower limit of sigma is equal to zero. There are cases where a confidence interval(Frequentist statistics) can also be equal to a credible interval (Bayesian statistics), and the statement would be correct.

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September 27, 2020 at 4:42 am #250177
Fausto Galetto
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@sks2

I try to see IF I understand correctly your statements.

You say:
- · “The wider the net you cast, the more often you’ll observe the true value.”
Do you mean that the “true value” is an observable quantity?

You say:
- · There are cases where a confidence interval (Frequentist statistics) can also be equal to a credible interval (Bayesian statistics), and the statement would be correct.
Do you mean that the statement “95% of the hamburgers have fat content with a standard deviation that is lower than 0.492 gram.” is correct only IF a credible interval is used (Bayesian statistics) AND confidence interval=credible interval, while it is wrong when we use “Frequency statistics” OR confidence interval is NOT=credible interval?

Thank you

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September 28, 2020 at 10:26 am #250212

MinitabUser1829
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Statement #2 seems a little odd, maybe even incorrect. I say maybe because I would need to see the statement in context. A confidence interval is not a statement about individual items (hamburgers), so statement #2 seems wrong on it’s surface.

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September 29, 2020 at 3:40 am #250235
Fausto Galetto
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@MinitabUser1829

The complete statement in the book about Statistics and Minitab is
- the upper bound is 0.492 gram for the standard deviation (given by the chi-square method). This means that 95% of the hamburgers have fat content with a standard deviation that is lower than 0.492 gram.
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