Question

To use the t-statistic to test for a difference between the means of two populations, what assumptions must be made about the two populations? About the two samples?

Short answer

The T Statistic is used in a T-test to determine whether to accept as well as deny the empty hypothesis.

Step-by-step solution

Step-by-Step Solution Step 1: Definition of t-test.

The t-test is a statistical test used to compare the means of two groups. It helps us to determine whether there is a significant difference between the mean of the two groups or not.

The formula of the t-test is:

$\mathbf{\text{t=}}\frac{\overline{\mathbf{\text{x}}}\mathbf{-}\mathbf{\text{μ}}}{\frac{\mathbf{\text{σ}}}{\sqrt{\mathbf{\text{n}}}}}$

Assumptions to be made about populations and samples.

The common assumptions made when doing a t-test include those regarding the scale of measurement, random sampling, normality of data distribution, adequacy of sample size, and equality of variance in standard deviation.

1. The observations in one sample are independent of the observations in the other sample.
2. Both samples are approximately normally distributed.
3. Both samples have approximately the same variance.
4. Both samples were obtained using a random sampling method.