Question

John Wayne Like a lot of other Americans. John Wayne died of cancer. But is there more to this story? In 1955. Wayne was in Utah shooting the film The Conqueror. Across the state line. in Nevada. the United States military was testing atomic bombs. Radioactive fallout from those tests drifted across the filming location. A total of 46 of the 220 people working on the film eventually died of cancer. Cancer experts estimate that one would expect only about 30 cancer deaths in a group this size.
a) Is the death rate among the movie crew unusually high?
b) Does this prove that exposure to radiation increases the risk of cancer?

Answer 1

Answer:-

Given that:-

The objective of the study is to know whether he death rate due to cancer in the movie crew is unusally high The parameter of interest is the proportion of people who die of cancer .Cancer experts estimate that one would expect only about 30 cancer deaths in a group of size 220 That is the proportion of expected deaths is

So the hypotheses to be testedare:

The conditiones are given by

Assumption:

Generally, the death of one person has no effecton the death of another person

Randomization Condition:

We have results for all 220 people working on the film.This is not a random sample and so we must be cautious about any general conclusions But we are interested in only the death rate in the movie crew So this may be reasonably representative of all the movie crews working in 10% Condition.

We are interesetd in death rate in the movie crew whille not a random sample these 220 people are fewer then 10% of all moviecrew members working in success/Failure Condition:

Both and are at least 10 Because the conditions are satisfied.we will use a model for the sampling distribution of the proportion and do a one - proportion z- test

Now, we can proceed further to do the test

We have n=220,X=46 and a hypothesized

So the observed proportion is:

The stanadrd deviation is given by

And the

The Z- value is given by,

The P- value is given by

P-value

Conclusion

P- value =0.0008 says that if the true proportion of cancer deaths were 0.1364 then the observed value of 2091(or larger) would occur less than 8 out of 10000 times

With the P - value that small ,we reject the null hypotheses H_{0} and hence, we may conclude that the true proportion of cancer deaths is greater than 13.64% and that the deaths rate obsreved in the movie crew is unusually high, assuming the group to be typical group of people

b) The sample Under study is the group of people who belong to a movie crew

This sample may not representative of the entire population

And so the results of this hypothesis test could not be generalized to make conclusions such as exposure to radition icreases the risk of cancer

The unusally high deaths rate in the group of people has nothing to do with the effect of radiation .The reason for this group to be atypical may be different from the radiation effecr.