Table 28-2
Suppose people in the adult population in a small country are classified based on their age.

Labor Force Status Age
Less than 55 55 and Older
Number employed 400,000 100,000
Number unemployed 25,000 7,000
Number in population 600,000 200,000

Refer to Table 28-2. In the proper order, which age group has the highest unemployment rate and which has the highest labor-force participation rate?

Question

Table 28-2
Suppose people in the adult population in a small country are classified based on their age.

​

Labor Force Status	Age
Less than 55	55 and Older
Number employed	400,000	100,000
Number unemployed	25,000	7,000
Number in population	600,000	200,000

​

Refer to Table 28-2. In the proper order, which age group has the highest unemployment rate and which has the highest labor-force participation rate?

BlackTom AI · Accepted Answer

First, restating the data helps us evaluate the two age groups:
- Under 55: Employed 400,000; Unemployed 25,000; Population 600,000.
- 55 and Older: Employed 100,000; Unemployed 7,000; Population 200,000.

Now, for each option, we analyze the unemployment rates and labor-force participation rates.

Option 1: "Under 55, 55 and older"
- This would claim the under-55 group has the highest unemployment rate and the 55-and-older group has the highest labor-force participation rate.
- Unemployment rate under 55 = 25,000 / (400,000 + 25,000) = 25,000 / 425,000 ≈ 5.88%.
- Unemployment rate 55 and Older = 7,000 / (100,000 + 7,000) = 7,000 / 107,000 ≈ 6.54%.
- Participation rate under 55 = 425,000 / 600,000 ≈ 70.8%.
- Participation rate 55 and Older = 107,000 / 200,000 = 53.5%.
- This option would imply the under-55 group has the higher unemployment rate, which is incorrect given the calculations above, and also that the older group has the higher participation rate, which is also incorrect. Therefore this option is false.

Option 2: "Under 55, under 55"
- This suggests both the highest unemployment rate and the highest participation rate belong to the under-55 group.
- As shown, the unemployment rate is lower for under 55 (≈5.88%) than for the older group (≈6.54%), so it cannot have the highest unemployment rate.
- The participation rate for under 55 is higher than for the older group, but the question asks for the correct pairing of highest unemployment rate and highest participation rate, not just one. Since the unemployment claim is false, this option is incorrect.

Option 3: "55 and older, under 55"
- This asserts the 55-and-older group has the highest unemployment rate and the under-55 group has the highest labor-force participation rate.
- Unemployment rate 55 and Older ≈ 6.54% is indeed higher than under 55 ≈ 5.88%, so this part is correct.
- Labor-force participation: under 55 ≈ 70.8% is higher than 55 and Older ≈ 53.5%, so this part is also correct.
- Since both components match the calculated values, this option correctly identifies the proper order.

Option 4: "55 and older, 55 and older"
- This would say the 55-and-older group has both the highest unemployment rate and the highest labor-force participation rate.
- While the 55-and-older group does have the highest unemployment rate, it does not have the highest labor-force participation rate, which actually belongs to the under-55 group. Therefore this option is incorrect.

In summary, evaluating each choice against the actual computed rates shows that only Option 3 correctly assigns: the 55-and-Older group with the higher unemployment rate, and the Under 55 group with the higher labor-force participation rate.

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