In 1965, data on the connection between radioactive waste exposure and cancer mortality was published. The data was collected from 9 counties that were located near an Atomic Energy Commission facility in Hanford, Washington. The data give the index of exposure and the cancer mortality rate during 1959-1964 for the nine counties affected. Higher index of exposure values represent higher levels of contamination.
Variable Description:
County :Name of county Exposure: Index of exposure
Mortality: Cancer mortality per 100,000 man-years∗ The data is as follows:
County Exposure Umatilla 2.49 Morrow 2.57
Gilliam 3.41 Sherman 1.25 W asco 1.62 HoodRiver 3.83
Portland 11.64 Columbia 6.41 Clatsop 8.34
Mortality 147.1 130.1 129.9
113.5
137.5 162.3 207.5 177.9 210.3
The regression output is at follows: Coefficients:
Estimate Std. Error
(Intercept) 114.716 8.046 Exposure 9.231 1.419
a) Predict the mortality rate for a county with an exposure rate of 1.25.
b) What is the residual for Sherman county?
c) Is there evidence that there is a significant relationship between exposure and mortality?
i. Write down the null and alternative hypotheses
ii. Calculate the appropriate t-statistic and degrees of freedom
iii. Calculate the p-value. If it’s off the edge of the chart, you may say “the p-value is greater than ***” or “the p-value is less than ***”.
iv. What do you conclude?
d) Do these data show that increased exposure to radioactive waste causes increased cancer mortality? If not, explain what other information you’d need or how you’d design a study to show this.