48.0k views
0 votes
The following results are for two independent samples taken from the two populations.

Sample 1

N1 = 80
x1 = 104
σ1 = 8.4

Sample 2

N2 = 70
x2 = 106
σ2 = 7.6

What is the value of the test statistic?

User Nazgob
by
7.2k points

1 Answer

4 votes

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.

User Snives
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories