Question

Peace Corps Volunteers. The Peace Corps is an independent U.S. government agency that provides trained volunteers for countries requesting assistance. According to Peacecorps.org, as of September 2012, volunteers currently serve in about 76 different host countries. The average age of a volunteer is about 28 years old. The following table reports the percentage of total volunteers serving by geographic region.

(a) Use the table to design a procedure for obtaining a stratified sample (with proportional allocation) of 50 Peace Corps volunteers.

(b) If stratified random sampling with proportional allocation is used to select the sample of 50 Peace Corps volunteers, how many would be selected from the Caribbean?

Short answer

Part (a)

Region	Sample Size	Sample
Africa	21	28, 2, 24, 9, 14, 6, 1, 12, 17, 30, 31, 33, 10, 26, 25, 5, 15, 32, 11, 4, 3
Latin America	11	36, 38, 43, 35, 37, 47, 39, 40, 46, 41, 48
Eastern Europe/ Central Asia	7	57, 49, 58, 50, 52, 51, 54
Asia	5	65, 64, 62, 66, 63
Caribbean	2	69, 70
North Africa/Middle East	2	71, 73
Pacific Islands	2	75, 76

Part (b) 2.

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

The average age of a volunteer is about 28 years old. The following table reports the percentage of total volunteers serving by geographic region.

Part (a) Step 2. Find the size of each region.

Africa:

$$\begin{gathered} 76\times 0.43=32.68 \\ \approx 33 \end{gathered}$$

Latin America:

$$\begin{gathered} =76\times 0.21=15.96 \\ \approx 16 \end{gathered}$$

Eastern Europe/ Central Asia:

$$\begin{gathered} 76\times 0.15=11.4 \\ \approx 12 \end{gathered}$$

Asia:

$$\begin{gathered} 76\times 0.10=7.6 \\ \approx 8 \end{gathered}$$

Caribbean:

$$\begin{gathered} 76\times 0.04=3.04 \\ \approx 3 \end{gathered}$$

North Africa/Middle East:

$$\begin{gathered} 76\times 0.04=3.04 \\ \approx 3 \end{gathered}$$

Pacific Islands:

$$\begin{gathered} 76\times 0.03=2.28 \\ \approx 2 \end{gathered}$$

Part (a) Step 3. Calculate the sample from each stratum.

The sample size for the stratum "Africa":

$$\begin{gathered} 50\times 0.43=21.5 \\ \approx 21 \end{gathered}$$

The sample size for the stratum "Latin America":

$$\begin{gathered} 50\times 0.21=10.5 \\ \approx 11 \end{gathered}$$

The sample size for the stratum "Eastern Europe/ Central Asia":

$$\begin{gathered} 50\times 0.15=7.5 \\ \approx 7 \end{gathered}$$

The sample size for the stratum "Asia":

$50\times 0.10=5$

The sample size for the stratum "Caribbean":

$50\times 0.04=2$

The sample size for the stratum "North Africa/Middle East":

$50\times 0.04=2$

The sample size for the stratum "Pacific Islands":

$$\begin{gathered} 50\times 0.3=1.5 \\ \approx 2 \end{gathered}$$

Part (a) Step 4. Obtain a sample of size 50, use stratified sampling.

Separate the population into strata (regions).

There are seven strata in this circumstance, with sizes of 33, 16, 12, 6, 3, 3, and 3.

Volunteers 1-33 make up stratum #1, whereas volunteers 34-48 make up stratum #2.

Volunteers in stratum #3 range from 49 to 60, volunteers in stratum #4 range from 61 to 66, volunteers in stratum #5 range from 67 to 70, volunteers in stratum #6 range from 71 to 73, and volunteers in stratum #7 range from 74 to 76.

For each stratum, create a basic random sample using the sample size specified in the table. To get 21 members from stratum #1, use MINITAB.

Procedure for MINITAB:

Step 1: Select Calc > Random Data > Integer from the menu bar.

Step 2: Double your selected sample size in the Number of rows of data to generate a section, just in case there are repeats. Set the sample size to 21.

Step 3: In the Store in the column, type Stratum 1 in column C1.

Step 4: Enter 1 as the minimum value.

Step 5: Enter 33 as the maximum value.

Step 6: Press the OK button.

MINITAB output

Stratum 1:

28 2 24 9 14 6 1 12 17 30 31 33 10 26 25 5 15 32 11 4 3.

Part (a) Step 5. To obtain a sample of size 50, use stratified sampling.

Similarly, follow the MINITAB approach to find participants for each location.

Change the sample size, minimum value, and maximum value for each region in the MINITAB method.

Stratum 2:

36 38 43 35 37 47 39 40 46 41 48

Stratum 3:

57 49 58 50 52 51 54

Stratum 4:

65 64 62 66 63

Stratum 5:

69 70

Stratum 6:

71 73

Stratum 7:

75 76

Part (b) Step 1. Determine the number of volunteers from the Caribbean who will be chosen.

Part (a) indicates that the number of volunteers to be chosen from the Caribbean is two.