Select the analysis options for 1-Sample Poisson Rate

Stat > Basic Statistics > 1-Sample Poisson Rate > Options

Specify the confidence level for the confidence interval, select the alternative hypothesis, specify the method for the test and confidence interval, or specify the length of observation.

Confidence level

In Confidence level, enter the level of confidence for the confidence interval.

Usually, a confidence level of 95% works well. A 95% confidence level indicates that, if you take 100 random samples from the population, the confidence intervals for approximately 95 of the samples will contain the population parameter.

For a given set of data, a lower confidence level produces a narrower confidence interval, and a higher confidence level produces a wider confidence interval. The width of the interval also tends to decrease with larger sample sizes. Therefore, you may want to use a confidence level other than 95%, depending on your sample size.
  • If your sample size is small, a 95% confidence interval may be too wide to be useful. Using a lower confidence level, such as 90%, produces a narrower interval. However, the likelihood that the interval contains the population rate decreases.
  • If your sample size is large, consider using a higher confidence level, such as 99%. With a large sample, a 99% confidence level may still produce a reasonably narrow interval, while also increasing the likelihood that the interval contains the population rate.

Alternative hypothesis

From Alternative hypothesis, select the hypothesis that you want to test.
Rate < hypothesized rate

Use this one-sided test to determine whether the population rate of occurrence is less than the hypothesized rate, and to get an upper bound. This one-sided test has greater power than a two-sided test, but it cannot detect whether the population rate is greater than the hypothesized rate.

For example, an analyst uses this one-sided test to determine whether the rate of televisions that customers return per month is less than 3. This one-sided test has greater power to determine whether the rate is less than 3, but it cannot detect whether the rate is greater than 3.

Rate ≠ hypothesized rate

Use this two-sided test to determine whether the population rate differs from the hypothesized rate, and to get a two-sided confidence interval. A two-sided test can detect differences that are less than or greater than the hypothesized value, but it has less power than a one-sided test.

For example, an analyst tests whether the rate of maintenance problems for a type of aircraft is different from the target of 0.2 per day. Because any difference from the target is important, the analyst tests whether the difference is greater than or less than the target.

Rate > hypothesized rate

Use this one-sided test to determine whether the population rate of occurrence is greater than the hypothesized rate, and to get a lower bound. This one-sided test has greater power than a two-sided test, but it cannot detect whether the population rate is less than the hypothesized rate.

For example, a call center manager uses this one-sided test to determine whether the rate of calls per day is greater than 1000. This one-sided test has greater power to determine whether the rate is greater than 1000, but it cannot determine whether the rate is less than 1000.

For more information on selecting a one-sided or two-sided alternative hypothesis, go to About the null and alternative hypotheses.

Method

From Method, select the method to use to calculate the hypothesis test and confidence interval. By default, Minitab uses the exact method because it is more accurate and powerful. However, many statistics textbooks use the normal approximation method because it is easier for students to calculate manually.

Length of observation

Enter a value to specify the observation period (time, area, volume, number of items) for the count data. By default, Minitab uses a value of 1, but you can enter a different value to represent the sample rate of occurrence in a more useful form.

For example, inspectors inspect the number of defects in a box of towels. A towel can have more than one defect, such as 1 tear and 2 pulls (3 defects). Each box contains 10 towels. The inspectors sample 50 total boxes, and find a total of 122 defects.
  • To determine the number of defects per box, the analyst uses a length of observation of 1. The rate of occurrence Minitab uses in the analysis is 122/50 = 2.44.
  • To determine the number of defects per towel, the analyst uses a length of observation of 10. The rate of occurrence Minitab uses in the analysis is (122/50)/10 = 0.244.
Note

If you enter a length of observation other than 1, convert the Hypothesized rate. For example, if your unconverted hypothesized rate is 15 defects per quarter and your length of observation is 3, enter the converted rate of 5 (15 ÷ 3) defects per month for the Hypothesized rate.

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