Question 1

In a criminal trial,a Type I error is made when an innocent person is convicted.

Accepted Answer

A Type I error in a criminal trial is also known as a false positive, which means an innocent person is wrongly convicted.

Question 2

The probability of a Type I error is denoted by:

Accepted Answer

The probability of a Type I error is denoted by α. This type of error occurs when we reject a true null hypothesis. The probability of a Type II error is denoted by β, which occurs when we fail to reject a false null hypothesis. Therefore, the best choice is C, α.

Question 3

A null hypothesis is a statement about the value of a population parameter.

Accepted Answer

This is correct. A null hypothesis is a declarative statement that represents a population characteristic, such as the mean or proportion, and is treated as true until statistical evidence suggests otherwise.

Question 4

A Type II error is committed if we make:

Accepted Answer

A Type II error occurs when we fail to reject a false null hypothesis, which means making an incorrect decision when the null hypothesis is false.

Question 5

A Type II error is represented by α; it is the probability of rejecting a true null hypothesis.

Accepted Answer

A Type II error is represented by β, and it is the probability of failing to reject a false null hypothesis. α represents the probability of a Type I error, which is rejecting a true null hypothesis.

Question 6

A Type II error is represented by  ; it is the probability of failing to reject a false null hypothesis.

Accepted Answer

This statement correctly defines a Type II error as the probability of failing to reject a false null hypothesis.

Question 7

The probability of making a Type I error and the level of significance are the same.

Accepted Answer

The probability of making a Type I error, also known as the significance level, is typically set by the researcher before conducting the statistical test. Therefore, the two terms are synonymous, and the probability of making a Type I error and the level of significance are the same.

Question 8

Reducing the probability of a Type I error also reduces the probability of a Type II error.

Accepted Answer

Reducing the probability of a Type I error may increase the probability of a Type II error, as the significance level (alpha) is lowered, leading to a higher threshold for rejecting the null hypothesis and potentially increasing the likelihood of accepting a false null hypothesis. Reducing the probability of a Type II error would require increasing the sample size or making other adjustments to increase the power of the study.

Question 9

A Type I error is represented by  .

Accepted Answer

The answer of A Type I error is represented by...

Question 10

In a criminal trial,a Type II error is made when an innocent person is acquitted.

Accepted Answer

A Type II error in the context of a criminal trial occurs when a guilty person is acquitted, not when an innocent person is acquitted.

Question 11

The hypothesis of most interest to the researcher is:

Accepted Answer

The alternative hypothesis is the one that the researcher wants to support or prove, therefore it is the one of most interest. The null hypothesis is usually the default or status quo assumption, so it is not necessarily of greater interest to the researcher.

Question 12

An alternative or research hypothesis is an assertion that holds if the null hypothesis is false.

Accepted Answer

An alternative hypothesis is indeed an assertion that stands true if the null hypothesis is rejected, which means it is false. So, the statement is true.

Question 13

The statement of the null hypothesis always includes an equals sign (=).

Accepted Answer

This is true, as the null hypothesis is typically structured to assume that there is no significant difference or effect, which can be represented by an equals sign.

Question 14

A professor of linguistics refutes the claim that the average student spends 3 hours studying for the midterm exam.She thinks they spend more time than that.Which hypotheses are used to test the claim?

Accepted Answer

The correct hypothesis to test the professor's claim is A) $H_0: \mu = 3$ vs. $H_1: \mu > 3$, where $H_0$ is the null hypothesis stating the average time spent is 3 hours, and $H_1$ is the alternative hypothesis suggesting students spend more than 3 hours, which aligns with the professor's belief.

Question 15

It is possible to commit a Type I error and a Type II error at the same time.

Accepted Answer

A Type I error occurs when a true null hypothesis is incorrectly rejected, while a Type II error happens when a false null hypothesis fails to be rejected. These errors are mutually exclusive outcomes of a hypothesis test.

Question 16

There is an inverse relationship between the probabilities of Type I and Type II errors; as one increases,the other decreases,and vice versa.

Accepted Answer

This statement is true according to statistics. When the probability of Type I error (rejecting a true null hypothesis) decreases, the probability of Type II error (failing to reject a false null hypothesis) increases, and vice versa. This is known as the power of a statistical test.

Question 17

In testing a hypothesis,statements for the null and alternative hypotheses as well as the selection of the level of significance should precede the collection and examination of the data.

Accepted Answer

It is important to establish the null and alternative hypotheses and select the level of significance before collecting and analyzing data to ensure a clear and structured approach to hypothesis testing.

Question 18

A Type I error is committed if we make:

Accepted Answer

A Type I error is also known as a false positive, meaning the null hypothesis is actually true, but we rejected it in favor of the alternative hypothesis. Therefore, making an incorrect decision when the null hypothesis is true results in a Type I error.

Question 19

Increasing the probability of a Type I error will increase the probability of a Type II error.

Accepted Answer

Increasing the probability of a Type I error (rejecting a true null hypothesis) actually decreases the probability of a Type II error (failing to reject a false null hypothesis), as these errors are inversely related.

Question 20

A Type I error is represented by α; it is the probability of rejecting a true null hypothesis.

Accepted Answer

A Type I error is indeed represented by α and it occurs when a researcher rejects a null hypothesis that is actually true. The probability of committing a Type I error is denoted by the symbol α.

Quiz 11: Introduction to Hypothesis Testing