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Chapter 18: Problem 43

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. Acrosss 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?

Short Answer

Expert verified
a) Based on the given data, yes, the death rate among the movie crew seems to be unusually high when compared to the expected rate. b) While the data could suggest a link between exposure to radiation and an increased risk of cancer, it does not definitively prove this connection, since other factors could have contributed to the increased rate and more extensive studies would be needed to substantiate this claim.

Step by step solution

01

Determine the Observed Cancer Death Rate

The first task is to determine the observed death rate among the movie crew. From the prompt, we know that 46 out of 220 individuals died of cancer. This can be expressed as a percentage by dividing the number who died (46) by the total number of individuals (220), and then multiplying by 100: \(\frac{46}{220} \times 100 = 20.9\%\). This is the observed death rate in the crew.
02

Determine the Expected Cancer Death Rate

Next, we need to compare this to the expected death rate in a similar population. The prompt gives us this information: in a group this size, one would expect roughly 30 cancer deaths. Using the same formula, we can determine the expected death rate: \(\frac{30}{220} \times 100 = 13.6\%\). This is the expected death rate in a similar-sized group.
03

Compare the Observed and Expected Rates

Now that we have both rates, we can compare them. The observed rate (20.9%) is more than the expected rate (13.6%), which does suggest that the death rate amongst the movie crew might be unusually high. This supports the first part of the exercise.
04

Evaluate the Evidence

To determine the second part of the exercise, asking if this proves that exposure to radiation increases the risk of cancer, we examine the evidence. While the observed rate is higher than the expected rate, correlation does not imply causation. Without more information, including other potential factors that could have contributed to this increased rate (such as lifestyle factors, genetic predisposition, etc.), it would be an overreach to definitively say that the exposure to radiation was the cause of the increased cancer risk. So, while this data might suggest a possible link, it does not prove that exposure to radiation increases the risk of cancer.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cancer Death Rate
Cancer death rates help us understand the frequency of cancer-related deaths within a specific population or group. In the case of John Wayne and the crew from "The Conqueror," we need to determine whether the number of deaths from cancer among the crew is higher than we would normally expect. Initially, we calculate the observed death rate by looking at the actual number of deaths. Here, 46 of the 220 crew members died of cancer. To express this as a percentage, you divide 46 by 220 and multiply by 100, resulting in an observed cancer death rate of 20.9%. Such analysis helps us see if a particular group's cancer rate is unusual and requires further investigation.
Observed vs Expected Rates
Understanding observed versus expected rates is crucial in hypothesis testing, especially in determining if an event's occurrence is common or rare. In this exercise: - The **observed rate** refers to the real or actual data collected, which is 20.9% in the movie crew case. - The **expected rate** relies on statistical expectations or averages. Here it is approximated at 13.6%. By comparing these rates, analysts can discern anomalies in data. If the observed rate significantly exceeds the expected rate, it suggests that unusual factors might be at play. This step points out that the cancer rate among the movie crew is indeed higher than anticipated, prompting further analysis.
Correlation vs Causation
The distinction between correlation and causation is fundamental in data analysis and scientific inquiry. Just because two events happen together does not prove one caused the other. In the film crew scenario: - A **correlation** exists between being on the crew and higher cancer rates, as observed rates exceeded expected rates. - But, establishing **causation**, or that radioactive exposure caused more cancer cases, requires more rigorous evidence. Without considering other factors, like genetics or lifestyle choices, one should not conclude that radiation exposure was definitively the cause. Correlation suggests a connection worth exploring further, but proving causation demands deeper research, possibly involving controlled studies, to rule out other variables.

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Most popular questions from this chapter

The College Board reported that \(60.3 \%\) of all students who took the 2016 AP Statistics exam earned scores of 3 or higher. One teacher wondered if the performance of her school was better. She believed that year's students to be typical of those who will take AP Stats at that school and was pleased when 34 of her 54 students achieved scores of 3 or better. a. How many standard deviations above the national rate did her students score? Does that seem like a lot? Explain. b. Can she claim that her school is better? Explain.

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