Q 8.25RP. - Elementary Statistics

Question

Wildfires. Wildfires are uncontrolled fires that usually spread quickly and are common in wilderness areas that have long and dry summers. The National Interagency Fine Center reports statistics on wildfires on their website www.nifc.gov. The following data lists the size, in thousands of acres, of a sample of $14$ large (at least $100,000$ acres) wildfires.

Use the technology of your choice to decide whether applying the one-mean $t-$interval procedure to these data is reasonable. Justify your answer.

Step-by-Step Solution

Answer

Using the $t-$interval approach to calculate a confidence interval for the population mean is not practical.

Step 1: Given information

341	414	907	163	161	220	113
500	316	102	131	125	517	240

Step 2: Explanation

Check whether obtaining a confidence interval for the population means using the $t-$interval approach is appropriate.

Draw the boxplot for the size of wildfires with MINITAB.

Procedure for MINITAB:

Step 1: Select Boxplot from the menu bar or Graph-Boxplot from the menu bar.

Step 2: Click OK after selecting Simple under One$Y\text{'}s$

Step 3: In the graph variables, fill in the SIZE data.

Step 4: Click the OK button.

OUTPUT FROM MINITAB: 

Step 3: Explanation

To create a normal probability plot for the size of wildfires, use MINITAB.

Procedure for MINITAB:

Step 1: Select Probability Plot from the Graph menu.

Step 2: Click OK after selecting Single.

Step 3: In the Graph variables section, add the SIZE column.

Step 4: Click the OK button.

OUTPUT FROM MINITAB: 

Step 4: Explanation

The following are the conditions for using the $t-$interval procedure:

Small Sample size:

• From the population, samples are drawn at random.
• The sample size is higher or the population follows a normal distribution.
• The standard deviation has not been determined.

It is evident from the MINITAB output that there is one outlier in the plot. The boxplot also shows that the distribution is biased to the right. As a result, the size distribution of wildfires deviates from the mean. Furthermore, the sample size is limited. As a result, using the $t-$interval approach to calculate a confidence interval for the population mean is not practical.