Final answer:
Yes, the t-test is still valid for nonmoral populations provided the sample size is large enough, due to the Central Limit Theorem. This theorem guarantees that the distribution of sample means approximates a normal distribution, thus allowing the use of the t-test.
Step-by-step explanation:
The student's question is whether the t-test of the population mean is still valid if the sampled population is nonmoral. The main answer is True. This principle is backed up by the Central Limit Theorem which states that, regardless of the population's distribution, the distribution of sample means will tend to be normal if the sample size is large enough. This is why it is possible to still use Student's t-test for hypothesis testing even when the population is not normally distributed, provided the sample size is sufficient.The condition that makes the t-test valid in cases of nonnormal populations relates to the sample size. According to the Central Limit Theorem for Sample Means (Averages), the distribution of sample means will become normal given a sufficiently large sample size. Thus, when performing a hypothesis test of a single population mean using a Student's t-distribution, it is crucial to ensure that the sample size is adequately large to approximate a normal distribution, even if the population distribution itself is skewed or otherwise nonmoral.Explanation in more than 100 words: The robustness of the t-test under the condition of a large sample size allows researchers to approximate the population standard deviation using the sample standard deviation. The test assumes that the sample means will equal the population mean, and that the standard deviation of the distribution of the sample means, or the standard error of the mean, will faithfully represent the variability within the population, ensuring a valid t-test.Conclusion: Essentially, the t-test remains a reliable method for hypothesis testing even for nonmoral populations, as long as the sample size is sufficiently large to invoke the Central Limit Theorem and approximate a normal distribution for the sample means.