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.

Open the sample data, CustomerComplaints.MTW.
Choose Stat > Basic Statistics > 1-Sample Poisson Rate.
From the drop-down list, select One or more samples, each in a column.
In Sample columns, enter Number of complaints.
Select Perform hypothesis test.
In Hypothesized rate, enter 10.
Select Options.
From Alternative hypothesis, select Rate > hypothesized rate.
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.

Method

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

Descriptive Statistics

N	Total Occurrences	Sample Rate	95% Lower Bound for λ
30	598	19.9333	18.6118

Test

Null hypothesis	H₀: λ = 10
Alternative hypothesis	H₁: λ > 10

P-Value
0.000