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Chapter 8: Problem 48

By establishing a small value for the significance level, are we guarding against the first type of error (rejecting the null hypothesis when it is true) or guarding against the second type of error?

Short Answer

Expert verified
By setting a small value for the significance level, we are guarding against the first type of error (rejecting the null hypothesis when it is true), also known as a Type I error. However, this increases the chances of committing a Type II error.

Step by step solution

01

Understand the significance level and its role in hypothesis testing

The significance level, often denoted as \(\alpha\), is a threshold that we set for the p-value of our test statistic. If the p-value is less than \(\alpha\), we reject the null hypothesis. It gives the probability of rejecting the null hypothesis when it is true, leading to a Type I error.
02

Understand Type I and Type II errors

A Type I error occurs when the null hypothesis is rejected when it is true. This is also knowned as a 'false positive'. A Type II error, on the other hand, occurs when the null hypothesis is not rejected when it is false. This is also knowned as a 'false negative'.
03

Relate the significance level and Type I error

By setting a small value for the significance level, we are making it harder to reject the null hypothesis. Therefore, we are reducing the likelihood of a Type I error (rejecting the null hypothesis when it is true). However, when we decrease the probability of Type I error, we increase the probability of Type II error (failing to reject the null hypothesis when it is false).

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Most popular questions from this chapter

The percentage of female CEOs in 2013 in Fortune 500 companies was \(4 \%\), according to Time magazine (March 18,2013 ). Suppose a student did a survey of 250 randomly selected large companies (not Fortune 500 companies), and 15 of them had women CEOs. a. About how many of the 250 should we expect to have female CEOs if the proportion of female CEOs is \(4 \%\), as it is for the Fortune 500 companies? b. Carry out the first two steps of a hypothesis test that will test whether the population proportion of women CEOs is not \(0.04\).

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