What assumption is required when utilizing the t-distribution ?
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Answer: A. The sample are drawn from a normally distributed population.
Explanation
The student t-distribution specifically requires underlying normality to produce reliable probability estimates. Without this foundational assumption, the mathematical derivation of the test statistic fails completely. The t-test relies heavily on this distributional property to accurately evaluate sample means. William Sealy Gosset developed the t-distribution under the pseudonym Student for small samples. It resembles the standard normal distribution but has heavier tails to account for uncertainty. Degrees of freedom determine the exact shape and critical values of the t-distribution curve.
Researchers use this test when population variance is unknown and sample sizes are small. It is widely applied in clinical trials to compare the means of two treatment groups. Ensuring normality prevents false positive conclusions in academic and scientific research studies. Option b is incorrect because the population variance is typically unknown when using t. Option d describes an unbiased estimator property rather than the distributional requirement itself. Since option b is false, option c cannot possibly be the correct choice here.
- Subject
- Mathematics
- Category
- Statistics
- Topic
- —
- Difficulty
- medium
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