The amount of samples required is dependent on a few factors:
Most commonly assumed confidence level is 95% which is an alpha-risk of 0.05. Also in most cases the question is two-tailed so shown below is the corresponding z value.
What sample size (n), is needed to specify a 95% confidence interval of +/- 1.5 units from the mean?
Assuming a normal distribution, the set of data of widget lengths has a historical variance of 13.4.
In this case it is two-tailed and Z = 1.96
The variance is 13.4 mm (which is the standard deviation squared).
n = (1.962 * 13.4) / 1.52
n = 3.8416 * 13.4 / 16 = 51.477 / 2.25 = 22.87
n = 23 samples (always round up to next sample to ensure enough Power)
Use the sample size shown above with the exception of substituting the Poisson average in place of the standard deviation.
Poisson average = n*p-hat = mean (from the attribute c chart of the data)
There are many tutorials and calculators on the web. A few links/videos are shown below:
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