5.4.4 - Checking Normality

Using Normal Probability Plot to Check Normality Section

If the sample size is less than 30, one needs to use a Normal Probability Plot to check whether the assumption that the data come from a normal distribution is valid.

Normal Probability Plot
The Normal Probability Plot is a graph that allows us to assess whether or not the data comes from a normal distribution.
Note! This plot should be used as a guide for us to assess if the assumption that the data come from a normal distribution is valid or not. It should not be used to “test” an assumption.

Example 5-7: Rattlesnake Lengths Section

It is very time consuming to find rattlesnakes and nerve racking to measure them (for obvious reasons). A scientist randomly finds 12 snakes from the central Pennsylvania area and measures their length. The following twelve measurements in inches are obtained:

40.2, 43.1, 45.5, 44.5, 39.5, 38.5, 40.2, 41.0, 41.6, 43.1, 44.9, 42.8

Using the above data, find a 90% confidence interval for the mean length of rattlesnakes in the central Pennsylvania area.

Answer

Step 1 Check Conditions

Think about what conditions you need to check. The sample size is only 12. The scenario does not give us an indication that the lengths follow a normal distribution. Therefore, let's do a normal probability plot to check whether the assumption that the data come from a normal distribution is valid.

  Minitab: Creating a normal probability plot

To create a normal probability plot in Minitab:

  1. Enter the 12 measurements into one column (name it length for this example) or upload the snakes.txt file.
  2. Type or upload the data in the first column in Minitab.
  3. Choose Graph > Probability Plot

Here is the normal probability plot for the rattlesnake data. What do you conclude about whether they may come from a normal distribution?

Minitab output of the normality plot for the snake example.Since the points all fall within the confidence limits, it is reasonable to suggest that the data come from a normal distribution.

Step 2 Construct the CI

Now, we can proceed to find the 90% t-interval for the mean length of rattlesnakes in the central Pennsylvania area since even though the sample size is less than 30, the normality plot shows that the data may come from a normal distribution.

  Minitab: Find the t-interval using Minitab
  1. Enter the 12 measurements into one column (name it length for this example)
  2. Choose Stat > Basic Statistics > 1-Sample t
  3. Click on the variable (length for this example) and change to the desired confidence level

The Minitab output will provide the confidence interval. We get the following:

N Mean StDev SE Mean 90% CI
12 42.075 2.257 0.652 (40.905, 43.245)

View the video to see these steps within Minitab.

Video: Minitab: 90% Confidence Interval for Continuous Data in Minitab

Step 3 Interpret the Interval

We are 90% confidence that the population mean lengths of rattlesnakes is between 40.905 and 43.245 inches.