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.


λ: Poisson rate of Number of complaints
Exact method is used for this analysis.

Descriptive Statistics

Sample Rate95% Lower
Bound for λ


Null hypothesisH₀: λ = 10
Alternative hypothesisH₁: λ > 10