Which of the following is an example of choosing a random sample from a target population of 100 students of which 40 are boys and 60 are girls?
A. Choosing every other person on an alphabetical list of names.
B. Choosing every 10th person from the list
C. Separating the group into groups of boys and girls and randomly choosing 5 boys and 5 girls from each group.
D. Tossing a number cube for each name on the list and choosing those names that corresponded to a 2, 4, or 6.
I believe B. would be the answer you're looking for!
A. Choosing every other person on an alphabetical list of names is not an example of choosing a random sample. It would only include students whose names happen to fall on the chosen positions in the list, which may not be representative of the overall population.
B. Choosing every 10th person from the list could potentially be a random sample if the list is randomized. However, it may still miss out on certain groups or patterns within the population.
C. Separating the group into groups of boys and girls and randomly choosing 5 boys and 5 girls from each group is a good example of choosing a random sample. It ensures representation from both boy and girl groups.
D. Tossing a number cube for each name on the list and choosing those names that correspond to a 2, 4, or 6 could potentially result in a random sample, but it depends on the fairness and randomness of the number cube. If the number cube is not truly random, it may introduce bias in the sample selection.
So, the best example of choosing a random sample from the target population of 100 students would be C. Separating the group into groups of boys and girls and randomly choosing 5 boys and 5 girls from each group.
To choose a random sample from a target population, we need a method that ensures each individual in the population has an equal chance of being selected. Let's analyze each option:
A. Choosing every other person on an alphabetical list of names: This method does not guarantee a random sample since it relies on the alphabetical order of names. For example, if all the boys have names starting with the letter "A," they would be overrepresented in the sample.
B. Choosing every 10th person from the list: This method is not truly random because it systematically selects individuals based on a fixed interval of 10. It might introduce bias if there is any pattern or clustering in the population.
C. Separating the group into groups of boys and girls and randomly choosing 5 boys and 5 girls from each group: This method ensures a random sample by first separating the population into two groups (boys and girls) and then randomly choosing individuals from each group. It provides equal representation from both genders.
D. Tossing a number cube for each name on the list and choosing those names that corresponded to a 2, 4, or 6: This method introduces randomness by using a fair chance device (number cube). Each individual has an equal probability of being selected (1 in 2) if we consider a 6-sided cube. However, this method may leave out potential participants who correspond to other numbers on the cube, thereby not guaranteeing equal representation across the population.
Out of the given options, option C (separating the group into groups of boys and girls and randomly choosing 5 boys and 5 girls from each group) is the best example of choosing a random sample from a target population. It ensures equal representation from each gender while maintaining randomness in the selection process.