Difficulty: Hard

Average Score: 38%

What is one of the three assumptions of independent t-tests?

Rationale

Individuals in the sample were selected randomly.

Random selection is a fundamental assumption of independent t-tests, ensuring that the samples are representative of the populations from which they are drawn. This assumption helps to minimize bias and allows for the generalization of results to the broader population.

A (Individuals in the sample were selected randomly.) CORRECT

This choice correctly reflects one of the key assumptions of independent t-tests. Random selection of individuals promotes valid statistical inferences by ensuring that each participant has an equal chance of being included in the sample, thereby enhancing the reliability of the results.

B (The size of each sample from the population is greater than 30.) YOUR ANSWER

While larger sample sizes can improve the robustness of statistical tests, it is not a strict assumption of independent t-tests. The assumption is more concerned with the random selection and independence of samples rather than the specific size, although a sample size greater than 30 is often recommended for the central limit theorem to apply.

C (Individuals in the two samples can be meaningfully paired.) YOUR ANSWER

This statement pertains to paired t-tests rather than independent t-tests. In independent t-tests, the samples are considered separate and not paired, which allows for the comparison of means between two different groups without any inherent relationship between the individuals in each group.

D (The population samples have the same mean and standard deviation.) YOUR ANSWER

This choice misrepresents the assumptions of independent t-tests. While it is assumed that the populations have equal variances (homogeneity of variance), there is no requirement for the means to be the same. In fact, the test is designed to determine whether there is a significant difference between the means of the two groups.

Conclusion

The fundamental assumption of random selection in independent t-tests is essential for ensuring that the samples accurately represent their respective populations, facilitating valid and unbiased comparisons. While sample size, pairing, and population parameters are important considerations in statistical analysis, they do not directly align with the assumptions specific to independent t-tests. Understanding these assumptions is crucial for properly applying the test and interpreting its results.

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