Question

Radioactive fallout from testing atomic bombs drifted across a region. There were 220 people in the region at the time and 32 of them eventually died of cancer. Cancer experts estimate that one would expect only about 29 cancer deaths in a group this size. Assume the sample is a typical group of people. Find the test statistic and p

​a) Is the death rate observed in the group unusually​ high?

​b) Does this prove that exposure to radiation increases the risk of​ cancer?

Answer 1

a) We have to test, H0: p = 29/220 against H1: p > 29/220, where, p is the proportion of people who died because of exposure of radiation.

The test-statistic is, Z = , where, = 32/220 = 0.1455, p = 29/220 = 0.1318, n = 220.

Hence, Z = 0.6007.

Under H0, Z ~ N(0,1).

The p-value = P(Z > 0.6007) = 1 - P(Z < 0.6007) = 1 - (0.6007) = 1 - 0.726 = 0.274.

If we assume the level of significance to be 0.05, then p-value > level of significance, so we fail to reject H0.

a. The death rate observed in that group is not unusually high.

b. Since, we fail to reject the null hypothesis, there is not enough evidence to conclude that exposure to radiation increases the risk of cancer.