Question 1

In a criminal trial, a Type II error is made when:
A)a guilty defendant is acquitted.
B)an innocent person is convicted.
C)a guilty defendant is convicted.
D)an innocent person is acquitted.

Accepted Answer

A Type II error is when a false negative occurs, meaning that the null hypothesis (in this case, the defendant being innocent) is accepted when it is actually false. Therefore, in the context of a criminal trial, a Type II error would occur if a guilty defendant is acquitted, which is option A.

Question 2

A Type I error occurs when we:
A)reject a false null hypothesis.
B)reject a true null hypothesis.
C)don't reject a false null hypothesis.
D)don't reject a true null hypothesis.

Accepted Answer

A Type I error occurs when we reject a true null hypothesis, meaning that we conclude there is a significant effect or difference when in reality there is none. This is also known as a "false positive" result.

Question 3

A Type II error is committed if we make:
A)a correct decision when the null hypothesis is false.
B)a correct decision when the null hypothesis is true.
C)an incorrect decision when the null hypothesis is false.
D)an incorrect decision when the null hypothesis is true.

Accepted Answer

The answer of A Type II error is committed if...

Question 4

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? A)H₀: $\mu$$\neq$ 3 vs. H₁: $\mu$ >3 B)H₀: $\mu$=3 vs. H₁: $\mu$$\neq$ 3 C)H₀:$\mu$$\neq$ 3 vs. H₁: $\mu$=3 D)H₀: $\mu$= 3 vs. H₁: $\mu$< 3

Accepted Answer

The answer of A professor of linguistics refutes the claim...

Question 5

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

Accepted Answer

The null hypothesis always includes an equals sign (=) because it is a statement that there is no significant difference or relationship between variables being compared. The alternative hypothesis, on the other hand, may or may not include an equals sign depending on the research question being asked.

Question 6

We cannot commit a Type I error when the:
A)null hypothesis is true.
B)level of significance is 0.10.
C)null hypothesis is false.
D)test is a two-tail test.

Accepted Answer

A Type I error occurs when we incorrectly reject a true null hypothesis. If the null hypothesis is false, then rejecting it is the correct decision, and a Type I error cannot occur.

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 and the level of significance represent the same thing, which is the probability of rejecting a true null hypothesis. Therefore, they are numerically equivalent and interchangeable.

Question 8

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, meaning that the prosecution incorrectly concludes that the defendant is guilty when they are actually innocent.

Question 9

In a criminal trial, a Type I error is made when:
A)a guilty defendant is acquitted.
B)an innocent person is convicted.
C)a guilty defendant is convicted.
D)an innocent person is acquitted.

Accepted Answer

A Type I error, also known as a false positive, occurs when an innocent person is wrongly convicted.

Question 10

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

Accepted Answer

This is the correct definition of a Type II error.

Question 11

Which of the following conclusions is not an appropriate conclusion from a hypothesis test? A)Reject H₀. Sufficient evidence to support H₁. B)Fail to reject H₀. Insufficient evidence to support H₁. C)Accept H₀. Sufficient evidence to support H₀. D)All of these choices are true.

Accepted Answer

Accepting the null hypothesis (H₀) does not provide evidence for any alternative hypothesis, so stating that accepting the null hypothesis provides sufficient evidence to support it is not an appropriate conclusion.

Question 12

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 is true. As the probability of making a Type I error (rejecting a true null hypothesis) decreases, the probability of making a Type II error (failing to reject a false null hypothesis) increases, and vice versa. This is known as the "power" of a statistical test, which is the probability of correctly rejecting a false null hypothesis.

Question 13

The probability of a Type I error is denoted by:
A)$\beta$
B)1- $\beta$
C)$\alpha$
D)1 - $\alpha$

Accepted Answer

The probability of a Type I error is denoted by α.

Question 14

A Type I error is committed if we make:
A)a correct decision when the null hypothesis is false.
B)a correct decision when the null hypothesis is true.
C)an incorrect decision when the null hypothesis is false.
D)an incorrect decision when the null hypothesis is true.

Accepted Answer

A Type I error occurs when we reject the null hypothesis when it is actually true.

Question 15

A Type II error is defined as:
A)rejecting a true null hypothesis.
B)rejecting a false null hypothesis.
C)not rejecting a true null hypothesis.
D)not rejecting a false null hypothesis.

Accepted Answer

A Type II error occurs when the null hypothesis is not rejected even though it is false. This means that the error is in failing to identify an effect or difference that actually exists.

Question 16

The probability of a Type II error is denoted by:
A)$\alpha$
B)$\beta$
C)1 - $\alpha$
D)1- $\beta$

Accepted Answer

The probability of a Type II error is denoted by β. Choice B is the only option that includes β.

Question 17

The hypothesis of most interest to the researcher is:
A)the alternative hypothesis.
B)the null hypothesis.
C)both hypotheses are of equal interest.
D)Neither hypothesis is of interest.

Accepted Answer

The alternative hypothesis is the one that the researcher wants to prove or support, making it the hypothesis of most interest. The null hypothesis, on the other hand, is the one that is tested against the alternative hypothesis and is usually the one assumed to be true until proven otherwise.

Question 18

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 19

A spouse suspects that the average amount of money spent on Christmas gifts for immediate family members is above $1,200. The correct set of hypotheses is: A)H₀: $\mu$=1200 vs. H₁: $\mu$<1200 B)H₀: $\mu$> 1200 vs. H₁: $\mu$= 1200 C)H₀:$\mu$=1200 vs. H₁:$\mu$> 1200 D)H₀: $\mu$ <1200 vs. H₁: $\mu$= 1200

Accepted Answer

The null hypothesis (H0) should always contain an equality sign, in this case, it is that the average amount spent on Christmas gifts for immediate family members is equal to $1,200. The alternative hypothesis (Ha) should contain the inequality sign representing the claim of the spouse, in this case, it is that the average amount spent on Christmas gifts for immediate family members is above $1,200. Therefore the correct set of hypotheses is H₀: F1F1F1S1μF1F1F10 F1F1F1S1=F1F1F10 1200 vs. H₁: F1F1F1S1μF1F1F10 F1F1F1S1>F1F1F10 1200. Choice C meets these requirements.

Question 20

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

This is the correct order of steps in hypothesis testing. The null and alternative hypotheses should be stated and the level of significance chosen before any data is collected or examined.

Quiz 11: Introduction to Hypothesis Testing

In a criminal trial, a Type II error is made when:

A Type I error occurs when we:

A Type II error is committed if we make:

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?

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

We cannot commit a Type I error when the:

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

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

In a criminal trial, a Type I error is made when:

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

Which of the following conclusions is not an appropriate conclusion from a hypothesis test?

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

The probability of a Type I error is denoted by:

A Type I error is committed if we make:

A Type II error is defined as:

The probability of a Type II error is denoted by:

The hypothesis of most interest to the researcher is:

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

A spouse suspects that the average amount of money spent on Christmas gifts for immediate family members is above $1,200. The correct set of hypotheses is:

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.

Quiz 11: Introduction to Hypothesis Testing

In a criminal trial, a Type II error is made when:

A Type I error occurs when we:

A Type II error is committed if we make:

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?

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

We cannot commit a Type I error when the:

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

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

In a criminal trial, a Type I error is made when:

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

Which of the following conclusions is not an appropriate conclusion from a hypothesis test?

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

The probability of a Type I error is denoted by:

A Type I error is committed if we make:

A Type II error is defined as:

The probability of a Type II error is denoted by:

The hypothesis of most interest to the researcher is:

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

A spouse suspects that the average amount of money spent on Christmas gifts for immediate family members is above $1,200. The correct set of hypotheses is:

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.

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