Question

Does the amount of hazardous material absorbed by the bodies of hazardous waste workers depend on gender? The level of lead in the blood was determined for a sample of men and a sample of women who dispose of hazardous waste as a full time job. You want to test the hypotheses that the amount absorbed by men is greater than the amount absorbed by women. After performing a hypothesis test for two independent samples, you see a p-value of 0.0032. Of the following, which is the appropriate conclusion?

1)The average amount of lead absorbed by men is significantly greater than the average amount of lead absorbed by women.

2)The average amount of lead absorbed by men is significantly less than the average amount of lead absorbed by women.

3)We did not find enough evidence to say the average amount of lead absorbed by men is greater than the average amount of lead absorbed by women.

4)The average amount of lead absorbed by men is less than or equal to the average amount of lead absorbed by women.

5)The average amount of lead absorbed by men is significantly different from the average amount of lead absorbed by women

Answer 1

Correct option is (A).

Explanation:

A two-sample t-test can be performed to determine whether the amount of hazardous material absorbed by the bodies of hazardous waste workers depend on gender or not.

Th hypothesis will be:

H₀: The amount absorbed by men is same as the amount absorbed by women, i.e. μ₁ = μ₂.

Hₐ: The amount absorbed by men is greater than the amount absorbed by women, i.e. μ₁ > μ₂.

The test statistic used is:

`t=\frac{\bar x_(1)-\bar x_(2)-(\mu_(1)-\mu_(2))}{\sqrt{(s_(1)^(2))/(n_(1))+(s_(2)^(2))/(n_(2))}}`

The decision rule to reject the null hypothesis based on the p-value is:

If the p-value of the test is less than the significance level α then the null hypothesis will be rejected. And if the p-value of the test is greater than the significance level α then the null hypothesis will not be rejected.

The p-value of the test is,

p - value = 0.0032

The commonly used significance levels are:

α = 0.01, 0.05 and 0.10.

The p-value of this test is less than all these α's.

Thus, the null hypothesis will be rejected.

Conclusion:

As the null hypothesis is rejected, it can be concluded that the amount of leas absorbed by men is significantly greater than the amount absorbed by women.

Thus, the correct option is (A).