# Example of 1-Sample Poisson Rate

A quality control manager for a city transportation department wants to improve customer satisfaction. To assess the current customer satisfaction level, the manager counts the number of customer complaints for 30 days.

The manager performs a 1-sample Poisson rate test to determine whether the average rate of complaints per day is greater than 10.

1. Open the sample data, CustomerComplaints.MTW.
2. Choose Stat > Basic Statistics > 1-Sample Poisson Rate.
3. From the drop-down list, select One or more samples, each in a column.
4. In Sample columns, enter Number of complaints.
5. Select Perform hypothesis test.
6. In Hypothesized rate, enter 10.
7. Select Options.
8. From Alternative hypothesis, select Rate > hypothesized rate.
9. Click OK in each dialog box.

## Interpret the results

The null hypothesis states that the rate is 10 complaints per day. Because the p-value of 0.000 is less than the significance level of 0.05 (denoted by α or alpha), the manager rejects the null hypothesis and concludes that the rate of complaints is greater than 10 per day.

### Test and CI for One-Sample Poisson Rate: Number of complaints

Method λ: Poisson rate of Number of complaints Exact method is used for this analysis.
Descriptive Statistics Total 95% Lower N Occurrences Sample Rate Bound for λ 30 598 19.9333 18.6118
Test Null hypothesis H₀: λ = 10 Alternative hypothesis H₁: λ > 10 P-Value 0.000
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