Question

Using Probability to Form Conclusions. In Exercises 37–40, use the given probability value to determine whether the sample results could easily occur by chance, then form a conclusion.

Cell Phones and Cancer A study of 420,095 Danish cell phone users resulted in 135 who developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute). When comparing this sample group to another group of people who did not use cell phones, it was found that there is a probability of 0.512 of getting such sample results by chance. What do you conclude?

Short answer

The probability that the given results are due to chance is 0.512.

There is insufficient evidence to conclude that cell phone users have a potential risk of developing cancer.

Step-by-step solution

Given information

Out of 420,095 cell phone users, 135 developed cancer (of the brain or nervous system).

There is a 0.512 probability of developing the disease by chance.

Define probability

Theprobability valueshows how likely a given event is in time. Its value ranges from 0 to 1 (inclusive).

When the probability is high, it implies that the occurrence of the event is highly likely. In case the probability is less than 0.05, the event is unusual.

Interpret the given value

The probability that the sample results occur in the study by luck is 0.512. This value is quite high.

It implies that the samples are highly likely to have occurred by chance in the study.

Thus, it cannot be concluded that cell phones result in the development of cancer of the brain and nervous system.