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Chapter 8: Problem 79

A researcher studying extrasensory perception (ESP) tests 300 students. Each student is asked to predict the outcome of a large number of coin flips. For each student, a hypothesis test using a \(5 \%\) significance level is performed. If the \(\mathrm{p}\) -value is less than or equal to \(0.05\), the researcher concludes that the student has ESP. Assuming that none of the 300 students actually have ESP, about how many would you expect the researcher to conclude do have ESP? Explain.

Short Answer

Expert verified
The researcher would incorrectly conclude that approximately 15 students out of 300 have ESP, due to the 5% significance level used in the hypothesis test.

Step by step solution

01

Understand the significance level

The significance level, also denoted as alpha \(\alpha\), is the probability of rejecting the null hypothesis when it is true. In this case, the null hypothesis is that the student does not have ESP. The significance level is set at 0.05, which means there is a 5% chance of falsely rejecting the null hypothesis.
02

Apply the significance level to the number of tests

The researcher is testing 300 students. If the null hypothesis is true for all students then, on average, we expect about 5% of them to still produce a p-value less than 0.05 purely by chance.
03

Calculate the expected number of false positives

To find out how many students we'd expect to incorrectly identify as having ESP, we multiply the total number of students by the probability of a false positive. So, the expected number of false positives is \(300 * 0.05 = 15\) students.

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Most popular questions from this chapter

Pew Research conducts polls on social media use. In \(2012,66 \%\) of those surveyed reported using Facebook. In 2018 , \(76 \%\) reported using Facebook. a. Assume that both polls used samples of 100 people. Do a test to see whether the proportion of people who reported using Facebook was significantly different in 2012 and 2018 using a \(0.01\) significance level. b. Repeat the problem, now assuming the sample sizes were both 1500 . (The actual survey size in 2018 was \(1785 .\) ) c. Comment on the effect of different sample sizes on the p-value and on the conclusion.

Dolly the Sheep, the world's first mammal to be cloned, was introduced to the public in 1997. In a Pew Research poll taken soon after Dolly's debut, \(63 \%\) of Americans were opposed to the cloning of animals. In a Pew Research poll taken 20 years after Dolly, \(60 \%\) of those surveyed were opposed to animal cloning. Assume this was based on a random sample of 1100 Americans. Does this survey indicate that opposition to animal cloning has declined since \(1997 ?\) Use a \(0.05\) significance level.

When a person stands trial for murder, the jury is instructed to assume that the defendant is innocent. Is this claim of innocence an example of a null hypothesis, or is it an example of an alternative hypothesis?

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