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Homework answers / question archive / With a population of 10,000 children ~(50% boys and 50% girls, 70% white and 30% nonwhite, and 57% single-parent family and 43% dual-parent family), what steps would you use to select a representative sample size of 150?
With a population of 10,000 children ~(50% boys and 50% girls, 70% white and 30% nonwhite, and 57% single-parent family and 43% dual-parent family), what steps would you use to select a representative sample size of 150?
The size of the representative sample is 150, or 1.5% of the overall population. Therefore, an ideal representative sample should be composed of the following:
50%, or 75 boys.
50%, or 75 girls.
70%, or 105 white children.
30%, or 45 nonwhite children.
57%, or 85-86 children from a single-parent family.
43%. or 64-65 children from a dual-parent family.
A random sample would be the best way to avoid bias in selecting individuals for the sample; however, such a sample may not be very representative--100 boys and 50 girls, for example.
Therefore, a better option would be a stratified random sample, where a certain number of members of a group will be selected, but the member selection will be random.
Based on the above information, there are eight unique groups within the children:
1) Male, a white child from a single-parent family
2) Male, a white child from a dual-parent family
3) Male, a non-white child from a single-parent family
4) Male, a non-white child from a dual-parent family
5) Female, a white child from a single-parent family
6) Female, a white child from a dual-parent family
7) Female, a non-white child from a single-parent family
8) Female, a non-white child from a dual-parent family
The percentages of each are as follows (number of children adjusted to fit 150 total):
1) 50% * 70% * 57% = ~20%, or 30 children
2) 50% * 70% * 43% = ~15%, or 23 children
3) 50% * 30% * 57% = ~8.5%, or 13 children
4) 50% * 30% * 43% = ~6.5%, or 9 children
5) 50% * 70% * 57% = ~20%, or 30 children
6) 50% * 70% * 43% = ~15%, or 23 children
7) 50% * 30% * 57% = ~8.5%, or 13 children
8) 50% * 30% * 43% = ~6.5%, or 9 children
Therefore, from the total overall group of 10,000 children, 30 children will be randomly selected from those who are male, white, and from a single-parent family. Children from the other seven groups will be similarly selected. While this is not as random as a completely random sample, it is a better representation of the population, while minimizing bias due to random selection within the group.
