Question

Does the amount of hazardous material absorbed by the bodies of hazardous waste workers depend on gender? You want to test the hypotheses that the amount absorbed by men (group 1) is different from the amount absorbed by women (group 2). A random sample of 212 male workers and 114 female workers showed an average lead absorption in the blood of 12.59 (SD = 1.897) and 12.75 (SD = 0.621), respectively (measured in micrograms/deciliter). Assuming that the population standard deviations are the same, perform a two independent samples t-test on the hypotheses Null Hypothesis: μ₁ = μ₂, Alternative Hypothesis: μ₁ ≠ μ₂. What is the test statistic and p-value of this test?

Question 3 options:

1)	Test Statistic: -0.875, P-Value: 0.3822

2)	Test Statistic: 0.875, P-Value: 0.3822

3)	Test Statistic: -0.875, P-Value: 0.8089

4)	Test Statistic: -0.875, P-Value: 0.1911

5)	Test Statistic: -0.875, P-Value: 1.8089

Answer 1

From the Hypothesis, we understand that we are conductiong a 2 tailed test.

Since the standard deviations are considered to be equal, we use pooled variance.

The degrees of freedom = n1 + n2 - 2 = 212 + 114 - 2 = 324

The Test Statistic is given as below

The p value (2 tailed), df = 324, using technology or excel is 0.3822

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Therefore Option 1: Test Statistic = -0.875, P - Value = 0.3822

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