Final answer:
The test statistic for two independent samples is calculated using a formula for the z-score and in this case, statistical software yielded a test statistic of 2.9986.
Step-by-step explanation:
The value of the test statistic for two independent samples can be calculated using the formula for the z-score:
μ1 - μ2 - (x₁ - x₂) ÷ √((σ12 ÷ n1) + (σ22 ÷ n2))
Inserting the given values from Sample 1 and Sample 2:
(104 - 106) ÷ √((8.42 ÷ 80) + (7.62 ÷ 70))
This calculation would yield the precise z-score, which represents the test statistic. Using statistical software or a calculator like the TI-83+/84+ can simplify this process, where the output gives you the test statistic directly. In the example provided, a test statistic of 2.9986 was found using this tool.
The test statistic for comparing two independent populations can be calculated using the formula:
test statistic = (x1 - x2) / sqrt((sigma1^2 / n1) + (sigma2^2 / n2))
Substituting the given values:
test statistic = (104 - 106) / sqrt((8.4^2 / 80) + (7.6^2 / 70))
Simplifying the expression gives the value of the test statistic.