**Try these parameter**** values****:**

**No Significant Difference**

param. pop1 pop2

mean: 3.75 3.00

variance: 1.00 1.00

pop size: 10.0 10.0

**Significant Difference**

param. pop1 pop2

mean: 4.00 3.00

variance: 1.00 1.00

pop size: 10.0 10.0

**Role of Variance**

param. pop1 pop2

mean: 4.00 3.00

variance: 2.00 1.00

pop size: 10.0 10.0

**Role of Population Size**

param. pop1 pop2

mean: 4.00 3.00

variance: 2.00 1.00

pop size: 20.0 20.0

The **t-test** is employed when one wishes to determine if two samples have statistically different means. The t statistic is calculated as:

where the pooled variance, , is calculated as:

If **t** is greater than the critical value, then the two samples have statistically different means. The **critical value** can be determined given the sample sizes, the level of significance chosen (typically *a *= 0.05), and a critical value table.

**Adjust the means, variances, and sample sizes to the right:**

Increasing the difference between the means of the samples will increase the t value; decreasing the difference will decrease the t value. Increasing the variance will decrease the t value, whereas decreasing the variance will increase the t value. Changing the population sizes will affect both the t value and the critical value.