Question

SELECT ALL THAT APPLY. In a population of 250 students, 60% are Whites, 20% are Latinos, 15% are Blacks, and 5% others. In a proportionate stratified random sample of 120, ______.

Answer 1

In a proportionate stratified sample of 120, there are 72 Whites, 24 Latinos, 18 Blacks and 6  others.

Proportionate Stratified Sample

A proportionate stratified sample is one in which the size of the strata in the sample is proportional to the size of the strata in the population; in other words, the chance of selecting a unit from a stratum depends on the relative size of that stratum in the population.

Calculating the Proportionate Stratified Sample

The given percentage of -

Whites = 60%

Latinos = 20%

Blacks = 5%

Strength of the sample = 120

⇒ Number of Whites = 60% of 120

= 0.6 × 120

=72

Number of Latinos = 20% of 120

= 0.2 × 120

=24

Proportionate Stratified Sample of Blacks and Others

Count of Blacks = 15 % of 120

= 0.15 × 120

= 18

Count of others = 5% of 120

= 0.05 × 120

6

Thus, in a Proportionate Stratified Sample of 120, 72 are Whites, 24 are Latinos, 18 are Blacks, and 6 are others.

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