# 1 and 2-Sample Poisson Rate - Confidence Level - Minitab/Excel

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#### mikethepenguin

Hello all I have been looking at the breakdowns.mtw file in minitab help and I have tried to calculate the 1-Sample Poisson Rate, 95% confidence interval. I just can't seem to get the same answer as minitab. Can anyone offer any help for hand calculations?

The data is below.

15, 16, 16,16, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 20, 21, 21, 21, 21,21, 21, 22, 22, 23, 23, 24, 25, 26, 26

Mean = 19.93

Variance 9.236781609
Standard deviation 3.039207398
95% confidence level (i used the t-table for this)2.045

Standard deviation/ Square root of (30) = 0.554880816

Confidence Interval (min, max)
= Mean - (2.045) * (0.5548)
=Mean + (2.045) * (0.5548)

18.79860206
21.0680646

The answers from Minitab are 18.3675, 21.5970

Can anyone help?

#### Miner

##### Forum Moderator
The mistake was in your calculation of standard deviation. You treated the data as if they were continuous. They are Poisson. Therefore the variance = mean, and the standard deviation is the square root of the mean (i.e., 4.465, not 3.039).

If you substitute 4.465 for 3.039 in your calculations, you will obtain the Minitab results.

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#### mikethepenguin

Thanks for that. Could you please show me the formula you used? I can't find it on minitab.

Having tried it on my calculator, for the lower interval I am getting 18.266 however the upper is 21.6 so I guess this is as close as I will get?

Last edited by a moderator:

#### Miner

##### Forum Moderator
You used the correct formula. The only difference is that the standard deviation of a Poisson distribution is equal to the square root of the mean.

#### Steve Prevette

##### Deming Disciple
Super Moderator
Confidence Interval (min, max)
= Mean - (2.045) * sqrt(Mean)
=Mean + (2.045) * sqrt(Mean)

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#### mikethepenguin

Hi guys I am still struggling to get the answer. I have followed both suggestions but for the "Min" I am not getting the same result.

Likewise I can't even workout how they did the 2-Sample Poisson Rate...

To save any confusion I have attached my working file.

#### Attachments

• Example.xlsx
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