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# One Sample Poisson Rate Help

The One Sample Poisson Rate technique is used to estimate the population rate of a Poisson distribution.  That estimate is then compared to a target value to determine if the estimated rate is different from the target value or not.  A confidence interval can be calculated to define a range of values that are likely to contain the rate.  This interval can be one or two sided.

The example below demonstrates how to do this test.  You can download the data at this link.

A customer service manager has been returning the number of returned goods per day.  He wants to know if the rate of returned goods is 10 returned goods per day.  He has collected data on the number of returned goods per day for 30 days. The steps to perform the analysis are given below.

1. Enter the data into a worksheet as shown below. The data must be in one column.

2. Select the data above (including the heading).

3. Select “Poisson Rate Tests” from the “Statistical Tools” panel in the SPC for Excel ribbon.

4. Select the “One Sample Poisson Rate.” The input form below is shown.

#### One Sample Poisson Rate Output

The output from the one sample Poisson rate technique is shown below.  In this example, the hypothesized rate is 10.  It is a two-side hypothesis test with alpha = 0.05.

An explanation of terms is given below the output.  In addition to the output table, the program displays two charts to help interpret the results.

The output tells you the conclusion from the test.  The null hypothesis (H0) and the alternate hypothesis (H1) are printed below the title.

The chart below is also created.  This makes it easy to see if the hypothesized rate is within the confidence interval or how far away it is from the confidence interval.

There is also a chart of the data to look for possible outliers.  If the program detects possible outliers, they will be in red and a message will be printed on the worksheet.

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