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Question 2 Consider the results of a prospective cohort study following a group of quarry employees working in an asbestos mine shown in Table .The researchers want to know if asbestos is a risk factor for lung cancer. The employees were broken into two groups. The exposed group consisted of miners who were exposed to high levels of asbestos on a day to day basis. The unexposed group consisted of quarry administrators, office workers, drivers and maintenance employees who were never exposed to high levels of asbestos Lung Cancer Outcome Present Absent Present 330 Asbestos Exposure Absent 543 a) Determine the Relative Risk, Attributable Risk b) Perform hypothesis testing to determine if there is a relative risk of lung cancer from asbestos exposure (a-0.05)

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Answer #1

a) The Relativerisk is computed as follows :

с/(c + d) 11/(11+543)

5.925

Inferable Risk (AR) is the distinction in the ailment rates in uncovered and unexposed people.

AR =44/(44+330)- 11/(11+543)= 0.0978


b) the accompanying cross tabilation have been given. the roe and section absolute have been determined and they are appeared as follows:

Total 374 554 928 Column 1 Column 2 Row 1 Row 2 Total 543 873

the normal qualities are figured as far as line and segment sums. truth be told, the equation is

where Ri compares to the all out entirety of components in roww I, Cj relates to the all out total of components in section j, and T is the excellent aggregate. the table beneath demonstrates the counts to get the table with anticipated qualities

Expected Values Column Column 2 Total 873 374/928 Row 1 55 374/928 22.166 374 351.834 873 554/928 Row 2 55 554/928 32.834 554 521.166 Total 873 928

In light of the watched and anticipated qualities, the squred separations can be registered by the accompanying equation

the table with squared separations is appeared as follows

Expected Values Column1 Total 873 374/928 351.834 Row 1 55 374/928 22.166 374 55 554/928 32.834 873 554/928 521.166 Row 2 554 Total 873 928

Null and Altemative Hypotheses The following null and alternative hypotheses need to be tested Ho: The two variables are independent H: The two variables are dependent This corresponds to a Chi-Square test of independence.

Rejection Region:  in view of the data gave the importance level α=0.05, the quantity of degrees opportunity is d f = (2-1) × (2-1) =1, so the dismissal area for this test is

R = {X : X > 3.841)

Test Statistics The Chi-Squared statistic is computed as follows: x2 = ý (o, EE,,)2 = 21.507+14.519+1.355 +0.915-38.296 i-1

Decision about the null hypothesis Since it is observed that X-38.296 > χ = 3.841, t is then concluded that the null hypothesis is rejected

End :

IT IS CONCLUDED THAT THE NULL HYPOTHESIS Ho is rejected. in this way, there is sufficient proof to guarantee that the two factors are needy, at the 0.05 essentialness level. so there is sufficient proof to guarantee that there is relative danger of lung cancer from asbestos introduction at 0.05 importance level

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