Question

Test the claim about the difference between two population means μ₁​ and μ₂​ at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed.

Claim: μ₁​=μ₂​; α=0.01

Population statistics: σ₁​=3.2, σ₂​=1.6

Sample statistics: x₁​=16, n₁​=30, x₂​=14, n₂​=28

Determine the standardized test statistic.
z=

Answer 1

The standardized test statistic, z, can be determined to test the claim about the difference between two population means μ₁​ and μ₂​ at a given level of significance α.

Step-by-step explanation:

To test the claim about the difference between two population means μ₁​ and μ₂​ at the level of significance α, we can use the standardized test statistic, z. The formula for the z-score is: z = ((x₁ - x₂) - (μ₁ - μ₂)) / (√((σ₁²/n₁) + (σ₂²/n₂)))

Using the given values, the standardized test statistic is: z = ((16 - 14) - (0)) / (√((3.2²/30) + (1.6²/28)))

After performing the calculations, the value of the standardized test statistic, z, is obtained.