A Statistics class from a high school with 4,000 students took a survey of the first 35 students who walked through the front door of the school, and asked how far they traveled to school that day. The class plans to run a one-sample t-test to determine if the average travel distance has increased since last year. The students notice that the sample data are right skewed. Which conditions have been satisfied for the t-test? I. The sample is from a random sample or randomized experiment. II. The sampling distribution of sample means is approximately normal. III. The sample size is small relative to the population.

Condition I is not satisfied because taking a survey of the first 35 students is not randomized sampling, and the students were not in an experiment.

Condition II is satisfied because the sample size of 35 > or = 30, and by Central Limit Theorem that means that the sampling distribution is approximately normal.

Condition III is satisfied because 35 is less than 10% of a reasonably sized high school's population.