Identify the distribution that applies to the following situation: In constructing a confidence interval of $\sigma$ you have 50 sample values and they appear to be
From a population with a skewed distribution.
A)Student t distribution
B)Normal distribution
C)Chi-square distribution
D)None of the three distributions is appropriate.

Question

Quizplus · Accepted Answer

The Student t distribution is used when the population standard deviation is unknown and the sample size is small (less than 30). In this case, the sample size is 50, which is greater than 30, so the Student t distribution is not appropriate. The normal distribution is used when the population standard deviation is known and the sample size is large (greater than 30). In this case, the population standard deviation is unknown, so the normal distribution is not appropriate. The chi-square distribution is used to test the goodness of fit of a distribution to data. In this case, we are not testing the goodness of fit of a distribution, so the chi-square distribution is not appropriate. Therefore, the only distribution that is appropriate is the Student t distribution.

Identify the Distribution That Applies to the Following Situation: in Constructing