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Chapter 4: Q40 (page 146)

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

Expert verified

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

01

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.

02

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.

03

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.

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Most popular questions from this chapter

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

Predicting Gender A study addressed the issue of whether pregnant women can correctly predict the gender of their baby. Among 104 pregnant women, 57 correctly predicted the gender of their baby (based on data from “Are Women Carrying ‘Basketballs’. . . ,” by Perry, DiPietro, Constigan, Birth, Vol. 26, No. 3). If pregnant women have no such ability, there is a 0.327 probability of getting such sample results by chance. What do you conclude?

Denomination Effect. In Exercises 13–16, use the data in the following table. In an experiment to study the effects of using four quarters or a \(1 bill, college students were given either four quarters or a \)1 bill and they could either keep the money or spend it on gum. The results are summarized in the table (based on data from “The Denomination Effect,” by Priya Raghubir and Joydeep Srivastava, Journal of Consumer Research, Vol. 36).

Purchased Gum

Kept the Money

Students Given Four Quarters

27

46

Students Given a $1 bill

12

34

Denomination Effect

a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.

b. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters.

c. What do the preceding results suggest?

Avogadro Constant If you are asked on a quiz to give the first (leftmost) nonzero digit of the Avogadro constant and, not knowing the answer, you make a random guess, what is the probability that your answer is the correct answer of 6?

In Exercises 13–20, express the indicated degree of likelihood as a probability value between 0 and 1.

Square Peg Sydney Smith wrote in “On the Conduct of the Understanding” that it is impossible to fit a square peg in a round hole.

In Exercises 21–24, use these results from the “1-Panel-THC” test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive results; among 157 negative results, there are 3 false negative results. (Hint: Construct a table similar to Table 4-1, which is included with the Chapter Problem.)

Testing for Marijuana Use

a. How many subjects are included in the study?

b. How many of the subjects had a true negative result?

c. What is the probability that a randomly selected subject had a true negative result?
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