Question 1

For a given level of significance, if the sample size is increased, the probability of committing a Type II error will increase.

Accepted Answer

The probability of committing a Type II error decreases as the sample size increases, assuming all other factors remain constant. This is because a larger sample size increases the power of the test to detect a true difference between groups, reducing the likelihood of failing to reject a false null hypothesis.

Question 2

One way of expressing how well a test performs is to report its power --the probability of detecting a false null hypothesis.

Accepted Answer

This statement is true. Power is the probability of correctly rejecting a false null hypothesis (i.e. detecting an effect that actually exists), and is often used as a measure of a test's performance.

Question 3

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 is committed when we reject the null hypothesis when it is actually true. This means we have made an incorrect decision when the null hypothesis is true, which is only true for option D.

Question 4

The operating characteristic curve plots the values of b (the probability of committing a Type II error)versus the values of the population mean m .

Accepted Answer

The operating characteristic curve plots the values of b (the probability of committing a Type II error) versus the values of the population mean m.

Question 5

The level of significance can be:
A)any number between - 1.0 and 1.0.
B)any number greater than zero.
C)any number greater than 1.96 or less than - 1.96.
D)None of these choices.

Accepted Answer

The level of significance is a value (usually denoted as alpha, α) that represents the probability of rejecting the null hypothesis when it is actually true. It is typically set at 0.05, 0.01, or another value depending on the context, but it is not defined by any of the ranges or specific numbers given in options A, B, or C.

Question 6

For a given sample size, the probability of committing a Type II error will increase when the probability of committing a Type I error is reduced.

Accepted Answer

This is because the two types of errors are inversely related. As the probability of committing a Type I error decreases, the probability of committing a Type II error increases, and vice versa. This is known as the "power" of a statistical test. A higher power indicates a lower probability of committing a Type II error, but a higher probability of committing a Type I error. Therefore, there is a trade-off between the two types of errors, and decreasing one will increase the other.

Question 7

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 8

The probability of a Type I error is denoted by:
A)b
B)1 - b
C)a
D)1 - a

Accepted Answer

The probability of a Type I error is denoted by alpha (α), which is represented by the letter 'a' in the given options. A Type I error occurs when a true null hypothesis is incorrectly rejected.

Question 9

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)H ₀: m = 1200 vs. H ₁: m 1200 B)H ₀: m > 1200 vs. H ₁: m = 1200 C)H ₀: m = 1200 vs. H ₁: m > 1200 D)H ₀: m 1200 vs. H ₁: m = 1200

Accepted Answer

The correct hypotheses for testing if the average amount is above $1,200 are: Null hypothesis (H0): m = 1200 (the average is $1,200) versus Alternative hypothesis (H1): m > 1200 (the average is greater than $1,200).

Question 10

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 is also known as a false positive, which means that the defendant is wrongly convicted or found guilty. Therefore, option B is the correct choice as an innocent person being convicted is an example of a Type I error.

Question 11

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 12

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 in the context of a criminal trial occurs when a guilty defendant is acquitted, meaning the error involves failing to reject a false null hypothesis (in this case, the hypothesis that the defendant is not guilty).

Question 13

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 we mistakenly conclude that there is a significant effect or difference when there actually isn't one. This is also known as a false positive or a “false alarm”.

Question 14

Which of the following conclusions is not an appropriate conclusion from a hypothesis test? A)Reject H ₀. Sufficient evidence to support H ₁. B)Fail to reject H ₀. Insufficient evidence to support H ₁. C)Accept H ₀. Sufficient evidence to support H ₀. D)All of these choices are true.

Accepted Answer

Accepting the null hypothesis (H0) simply means that there is not enough evidence to reject it, not that there is sufficient evidence to support it. Therefore, "Accept H ₀. Sufficient evidence to support H ₀" is not an appropriate conclusion.

Question 15

The power of a test is the probability that a true null hypothesis will be rejected.

Accepted Answer

The power of a test is actually the probability that it correctly rejects a false null hypothesis, not a true one.

Question 16

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)H ₀: m ¹ 3 vs. H ₁: m > 3 B)H ₀: m = 3 vs. H ₁: m ¹ 3 C)H ₀: m ¹ 3 vs. H ₁: m = 3 D)H ₀: m = 3 vs. H ₁: m 3

Accepted Answer

The correct hypothesis setup for testing if students spend more than 3 hours studying is to have the null hypothesis (H0) state the claim to be tested (in this case, m = 3) and the alternative hypothesis (H1) reflect the professor's belief (m > 3). However, due to a formatting error, the correct representation of the hypotheses is not clearly shown. The intended correct answer seems to be A, where the null hypothesis would typically be m = 3 (claim to be tested), and the alternative hypothesis would be m > 3 (professor's belief). The symbols and formatting are incorrect due to a transcription error, but the logic of choice A aligns most closely with the correct hypothesis testing approach.

Question 17

The probability of a Type II error is denoted by:
A)a
B)b
C)1 - a
D)1 - b

Accepted Answer

The probability of a Type II error is denoted by $ \beta $ (beta), which corresponds to failing to reject a false null hypothesis.

Question 18

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 involves failing to detect an effect or difference that actually exists.

Question 19

As the alternative value of m increases, so does the power of the test.

Accepted Answer

Increasing the alternative value of m typically increases the effect size, which can lead to a higher power of the test, meaning a greater probability of correctly rejecting the null hypothesis.

Question 20

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 typically the hypothesis of interest because it represents the possibility of a relationship or effect. It is the hypothesis the researcher hopes to support with evidence from the data. The null hypothesis, on the other hand, represents the absence of a relationship or effect and is typically used as a baseline for comparison. While the null hypothesis is still necessary for hypothesis testing, it is not typically of primary interest to the researcher.

Quiz 10: Introduction to Hypothesis Testing

For a given level of significance, if the sample size is increased, the probability of committing a Type II error will increase.

One way of expressing how well a test performs is to report its power --the probability of detecting a false null hypothesis.

A Type I error is committed if we make:

The operating characteristic curve plots the values of b (the probability of committing a Type II error)versus the values of the population mean m .

The level of significance can be:

For a given sample size, the probability of committing a Type II error will increase when the probability of committing a Type I error is reduced.

We cannot commit a Type I error when the:

The probability of a Type I error is denoted by:

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

A Type II error is committed if we make:

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

A Type I error occurs when we:

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

The power of a test is the probability that a true null hypothesis will be rejected.

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 probability of a Type II error is denoted by:

A Type II error is defined as:

As the alternative value of m increases, so does the power of the test.

The hypothesis of most interest to the researcher is: