## Related questions with answers

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?

Solutions

VerifiedIn this exercise, we will discuss the assumptions that must be met when we use the t-statistic to test for a difference between the means of two populations and two samples.

The conditions required for executing a hypothesis test using a $t$ test statistic are:

$\bullet$ The two samples are randomly selected from the populations.

$\bullet$ The two samples are independent.

$\bullet$ Both populations are approximately normally distributed.

$\bullet$ At least one of the samples is small: $n_1\leq 30$ or $n_2\leq 30$ (as otherwise we would use the $z$-test statistic)

$\text{\color{#4257b2}Note: There is no requirement for the variances of the two samples being equal or not, as we will use a $t$-test statistic in both cases.}$

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