Question

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

Answer 1

Independent of the unknown population standard deviation σ

Explanation:

It is one tailed test so the data is right skewed.

The t distribution approaches the standard normal distribution as the number of degrees of freedom or the sample size becomes larger.

Here the number of degrees of freedom in = n-1= 35- 1= 34

This is the only parameter of the t distribution.

The important property of t distribution is that it is independent of the unknown population standard deviation σ . It is therefore applied to test hypotheses about the mean of the population irrespective of what the standard deviation may be.