Revisiting the dust exposure study. The data on occupational exposure to dust that we analyzed in Exercise 1 come from two groups of workers that are quite different in size. This complicates pooling because the sample that is larger will dominate the calculations
(a) Find the pooled estimate of the standard deviation. Write a short summary comparing it with the estimates of the standard deviations that come from each group.
(b) Find the standard error of the difference in sample means that you would use for the method that does not assume equal variances. Do the same for the pooled approach. Compare these two estimates with each other.
(c) Perform the significance test and find the 95% confidence interval using the pooled methods. How do these results compare with those you found in Exercise 1?
Exercise 1
Dust exposure at work. Exposure to dust at work can lead to lung disease later in life. One study measured the workplace exposure of tunnel construction workers.26 Part of the study compared 115 drill and blast workers with 220 outdoor concrete workers. Total dust exposure was measured in milligram years per cubic meter (mg.y/m3). The mean exposure for the drill and blast workers was 18.0 mg.y/m3 with a standard deviation of 7.8 mg.y/m3. For the outdoor concrete workers, the corresponding values were 6.5 mg.y/m3 and 3.4 mg.y/m3.
(a) The sample included all workers for a tunnel construction company who received medical examinations as part of routine health checkups. Discuss the extent to which you think these results apply to other, similar types of workers.
(b) Use a 95% confidence interval to describe the difference in the exposures. Write a sentence that gives the interval and provides the meaning of 95% confidence.
(c) Test the null hypothesis that the exposures for these two types of workers are the same. Justify your choice of a one-sided or two-sided alternative. Report the test statistic, the degrees of freedom, and the P-value. Give a short summary of your conclusion.
(d) The authors of the article describing these results note that the distributions are somewhat skewed. Do you think that this fact makes your analysis invalid? Give reasons for your answer.