If a study does not require a mean and variance, what type of distribution is most likely indicated?

If a study does not require a mean and variance, what type of distribution is most likely indicated?

• A. T-distribution
• B. Normal distribution
• C. Poisson distribution
• D. Uniform distribution

Answer: (A)

When you’re estimating the population mean from a small sample and the population variance is unknown, you use the t distribution. Replacing the true standard deviation with the sample standard deviation introduces extra uncertainty, and the resulting test statistic follows a t distribution with degrees of freedom related to the sample size (often n−1). The t distribution has heavier tails than the normal, reflecting that extra variability, and it becomes increasingly similar to the normal distribution as the sample size grows. Other distributions describe different data situations: Poisson models counts with variance tied to the mean, the normal distribution applies when variance is known or the sample is large, and the uniform distribution assigns equal probability across an interval.

When you’re estimating the population mean from a small sample and the population variance is unknown, you use the t distribution. Replacing the true standard deviation with the sample standard deviation introduces extra uncertainty, and the resulting test statistic follows a t distribution with degrees of freedom related to the sample size (often n−1). The t distribution has heavier tails than the normal, reflecting that extra variability, and it becomes increasingly similar to the normal distribution as the sample size grows. Other distributions describe different data situations: Poisson models counts with variance tied to the mean, the normal distribution applies when variance is known or the sample is large, and the uniform distribution assigns equal probability across an interval.