Example of 1-Sample Poisson ratemain topic interpreting results session command see also
Example of 1-Sample Poisson rateCompany A manufactures televisions and has counted the number of units with defective screens they produce each quarter for the past ten years. Management decides that 20 defective units per quarter is the maximum acceptable rate, and they want to determine whether their factory meets this specification.
1 Open the worksheet TVDEFECT.MTW.
2 Choose Stat > Basic Statistics > 1-Sample Poisson Rate.
3 Choose One or more samples, each in a column.
4 In Sample columns, enter 'Defective A '.
4 Check Perform hypothesis test. In Hypothesized rate, enter 20.
5 Click Options. Under Alternative hypothesis, choose Rate < hypothesized rate.
6 Click OK in each dialog box.
Session window output
Test and CI for One-Sample Poisson Rate: Defective A
Test of rate = 20 vs rate < 20
Total Rate of 95% Upper Exact Variable Occurrences N Occurrence Bound P-Value Defective A 713 40 17.8250 18.9628 0.001
“Length” of observation = 1. |
The p-value for the one-tailed hypothesis test is 0.001. Therefore, you should reject the null hypothesis and conclude that the population defect rate is less than 20. You can further hone your estimate of the population rate by considering the 95% upper bound, which provides a value that the population defect rate is likely to be below. From this analysis, you can be reasonably confident that the number of defective screens per quarter is less than 18.9628. You conclude that televisions from Company A meet the company's quarterly defect specifications.