True or False The paired ttest has an assumption of normalit

True or False: The paired t-test has an assumption of normality or that the number of differences is more than 30

True or False: A paired t-test would be used in your experimental units are homogenous

True or False: If you have 20 pairs of observations for a paired t-test the degrees of freedom that would be used is 19

True or False: 2 sample t-tests can be used to analyze data collected from both experiments and surveys

Solution

1. False

The t-test assumes that the means of the different samples are normally distributed; it does not assume that the population is normally distributed.

By the central limit theorem, means of samples from a population with finite variance approach a normal distribution regardless of the distribution of the population. Rules of thumb say that the sample means are basically normally distributed as long as the sample size is at least 20 or 30. For a t-test to be valid on a sample of smaller size, the population distribution would have to be approximately normal.

The t-test is invalid for small samples from non-normal distributions, but it is valid for large samples from non-normal distributions.

2. True

3. True

It can be obtained by deducting no.of constraints from the total no.of observations in the sample.

df=(C-1)(N-1)

4. True

The independent two-sample t-test is used to test whether population means are significantly different from each other, using the means from randomly drawn samples.