Question

Military Assistance Loans. The annual update of U.S. Overseas Loans and Grants, informally known as the "Greenbook," contains data on U.S. government monetary economic and military assistance loans. The following table shows military assistance loans, in thousands of dollars, to a sample of $10$ countries, as reported by the U.S. Agency for International Development.

Short answer

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

Step-by-step solution

Given information

102	280	33	1643	177
69	180	89	205	695

Concept

The $t-$interval procedure will be used.

Explanation

Examine whether using the $t-$interval approach to construct a confidence interval for the population mean is appropriate.

To create a boxplot for military assistance loans, use MINITAB.

Procedure for MINITAB:

Step 1: Choose Graph$>$ Boxplot or Stat $>$EDA$>$Boxplot are the options.

Step 2: Select Simple under One Y's. Click OK.

Step 3: Fill in the data for Assistance loans in Graph variables.

Step 4: Click the OK button.

OUTPUT FROM MINITAB:

Explanation

To create a normal probability plot for military assistance loans, 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, type Assistance loans in the column.

Step 4: Click the OK button.

OUTPUT FROM MINITAB:

Explanation

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

Sample size is small:

- 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. Furthermore, the boxplot clearly shows that the distribution is biassed to the right. As a result, there is no regular distribution in the population. 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.