Question

Radioactive fallout from testing atomic bombs drifted across a region. There were 220 people in the region at the time and 48 of them eventually died of cancer. Cancer experts estimate that one would expect only about 32 cancer deaths in a group this size. Assume the sample is a typical group of people. ?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

Ans:

Given that

population proportion,p=32/220=0.1455

The null and alternative hypetheses are

Ho: p = 0.1455

Ha: p > 0.1455

sample proportion=48/220=0.2181

a)Test statistic:

z=(0.2181-0.1455)/sqrt(0.1455*(1-0.1455)/220)

z=3.06

p-value=P(z<3.06)=0.0011

As,probability is less than 0.05 the death rate observed in the group unusually high.

b)Assume signficance level=0.05

As,p-value<0.05,we reject the null hypothesis.

There is sufficient evidence to conclude that exposure to radiation increases the risk of cancer.