Question 1

If a researcher rejects a true null hypothesis, she has made a _______error.

Accepted Answer

Type I

Question 2

The power of a test is measured by its capability of
A) rejecting a null hypothesis that is true.
B) not rejecting a null hypothesis that is true.
C) rejecting a null hypothesis that is false.
D) not rejecting a null hypothesis that is false.

Accepted Answer

The power of a test refers to the ability of the test to correctly reject a null hypothesis that is false (i.e., to correctly detect a difference or relationship that exists in the population). Therefore, choice C is the correct option. Rejecting a null hypothesis that is true (choice A) is an error known as a type I error, whereas not rejecting a null hypothesis that is true (choice B) is a correct decision. Not rejecting a null hypothesis that is false (choice D) is an error known as a type II error.

Question 3

If an economist wishes to determine whether there is evidence that mean family income in a community exceeds $50,000
A) either a one-tail or two-tail test could be used with equivalent results.
B) a one-tail test should be utilized.
C) a two-tail test should be utilized.
D) None of the above.

Accepted Answer

A one-tail test should be utilized because the economist is interested in testing if the mean family income exceeds a specific value ($50,000), which is a directional hypothesis.

Question 4

If a researcher does not reject a true null hypothesis, she has made a _______decision.

Accepted Answer

The answer of If a researcher does not reject a...

Question 5

For a given level of significance ( $\alpha$ ), if the sample size n is increased, the probability of a Type II error ( $\beta$
 )
A) will decrease.
B) will increase.
C) will remain the same.
D) cannot be determined.

Accepted Answer

Increasing the sample size generally increases the power of a statistical test, which decreases the probability of a Type II error ($\beta$).

Question 6

Which of the following would be an appropriate null hypothesis?
A) The population proportion is less than 0.65.
B) The sample proportion is less than 0.65.
C) The population proportion is not less than 0.65.
D) The sample proportion is no less than 0.65.

Accepted Answer

A null hypothesis is a statement that we assume to be true until we have evidence to the contrary. In this case, the null hypothesis should be a statement about the population proportion, not the sample proportion. Option A and B are both incorrect because they're talking about sample proportion instead of population proportion. Option D might be true but it's not what we're trying to test, as we're interested in the population proportion. Therefore, the best choice is C, which is the opposite of what we want to prove, that the population proportion is less than 0.65.

Question 7

A Type II error is committed when
A) you reject a null hypothesis that is true.
B) you don't reject a null hypothesis that is true.
C) you reject a null hypothesis that is false.
D) you don't reject a null hypothesis that is false.

Accepted Answer

A Type II error occurs when a false null hypothesis is not rejected, meaning the error is in failing to identify an effect or difference when one actually exists.

Question 8

If the p-value is less than α in a two-tail test,
A) the null hypothesis should not be rejected.
B) the null hypothesis should be rejected.
C) a one-tail test should be used.
D) no conclusion should be reached.

Accepted Answer

A p-value less than α indicates that the probability of obtaining such a result by chance is very low. This provides evidence against the null hypothesis and supports the alternative hypothesis. Therefore, the null hypothesis should be rejected.

Question 9

Which of the following would be an appropriate alternative hypothesis?
A) The population proportion is less than 0.65.
B) The sample proportion is less than 0.65.
C) The population proportion is not less than 0.65.
D) The sample proportion is not less than 0.65.

Accepted Answer

The alternative hypothesis should state a direction or difference from the null hypothesis. Option A states that the population proportion is less than the null hypothesis value, which is a direction and therefore an appropriate alternative hypothesis. Options B and D are about the sample proportion, which is not the parameter being tested in the hypothesis test. Option C is not a direction or difference from the null hypothesis.

Question 10

Which of the following would be an appropriate alternative hypothesis?
A) The mean of a population is equal to 55.
B) The mean of a sample is equal to 55.
C) The mean of a population is greater than 55.
D) The mean of a sample is greater than 55.

Accepted Answer

An alternative hypothesis should propose that there is a difference or relationship between variables. Option C proposes that the mean of a population is greater than 55, suggesting a direction of difference from the null hypothesis. The other options propose equality between means, which is not appropriate for an alternative hypothesis.

Question 11

A Type I error is committed when
A) you reject a null hypothesis that is true.
B) you don't reject a null hypothesis that is true.
C) you reject a null hypothesis that is false.
D) you don't reject a null hypothesis that is false.

Accepted Answer

A Type I error occurs when the null hypothesis is actually true, but you reject it, leading to a false positive result or conclusion.

Question 12

Which of the following would be an appropriate null hypothesis?
A) The mean of a population is equal to 55.
B) The mean of a sample is equal to 55.
C) The mean of a population is greater than 55.
D) Only (a) and (c) are appropriate.

Accepted Answer

A is the only appropriate choice for a null hypothesis because it is a statement about the population parameter. B is incorrect because a sample mean cannot be a null hypothesis. C is incorrect because it suggests an alternative hypothesis, not a null hypothesis. D is also incorrect because C is not an appropriate null hypothesis.

Question 13

You know that the probability of committing a Type II error (β) is 5%, you can tell that the power of the test is
A) 2.5%
B) 95%.
C) 97.5%
D) unknown

Accepted Answer

The answer of You know that the probability of committing...

Question 14

If a test of hypothesis has a Type I error probability (α) of 0.01, it means that
A) if the null hypothesis is true, you don't reject it 1% of the time.
B) if the null hypothesis is true, you reject it 1% of the time.
C) if the null hypothesis is false, you don't reject it 1% of the time.
D) if the null hypothesis is false, you reject it 1% of the time.

Accepted Answer

A Type I error occurs when the null hypothesis is true, but we reject it anyway. With a Type I error probability (α) of 0.01, this means that if we were to conduct the same hypothesis test many times, and the null hypothesis were true each time, we would expect to reject the null hypothesis incorrectly about 1% of the time.

Question 15

You know that the level of significance ( $\alpha$ ) of a test is 5%, you can tell that the probability of committing a Type II error ( $\beta$
 ) is
A) 2.5%
B) 95%.
C) 97.5%
D) unknown

Accepted Answer

The level of significance ($\alpha$) is the probability of committing a Type I error, not Type II. The probability of a Type II error ($\beta$) depends on other factors like the true parameter value and sample size, and cannot be determined solely from $\alpha$.

Question 16

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

The probability of committing a Type II error and Type I error are inversely related. When the probability of committing a Type I error is reduced (i.e., lowering the significance level), the probability of committing a Type II error will increase (i.e., the power of the test will decrease).

Question 17

For a given sample size n, if the level of significance ( $\alpha$ ) is decreased, the power of the test
A) will increase.
B) will decrease.
C) will remain the same.
D) cannot be determined.

Accepted Answer

Decreasing the level of significance ($\alpha$) typically increases the probability of a Type II error ($\beta$), which in turn decreases the power of the test (1-$\beta$).

Question 18

If an economist wishes to determine whether there is evidence that mean family income in a community equals $50,000
A) either a one-tail or two-tail test could be used with equivalent results.
B) a one-tail test should be utilized.
C) a two-tail test should be utilized.
D) None of the above.

Accepted Answer

A two-tail test should be utilized because the economist is testing whether the mean family income is equal to a specific value ($50,000) and there is no prior reason to believe the income would be either higher or lower.

Question 19

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

Accepted Answer

The probability of committing a Type II error will decrease as the sample size increases because a large sample size increases the power of the test. Therefore, we are more likely to detect a true difference between the populations.

Question 20

For a given level of significance, if the sample size is increased but the summary
statistics remain the same, the probability of committing a Type I error will increase.

Accepted Answer

The probability of committing a Type I error is determined by the level of significance, not the sample size or summary statistics. Increasing the sample size without changing the summary statistics will improve the accuracy of the estimate and decrease the standard error, but it will not affect the probability of a Type I error.

Quiz 9: Fundamentals of Hypothesis Testing: One-Sample Tests

If a researcher rejects a true null hypothesis, she has made a _______error.

The power of a test is measured by its capability of

If an economist wishes to determine whether there is evidence that mean family income in a community exceeds $50,000

If a researcher does not reject a true null hypothesis, she has made a _______decision.

For a given level of significance ( $\alpha$ ) , if the sample size n is increased, the probability of a Type II error ( $\beta$ )

Which of the following would be an appropriate null hypothesis?

A Type II error is committed when

If the p-value is less than α in a two-tail test,

Which of the following would be an appropriate alternative hypothesis?

Which of the following would be an appropriate alternative hypothesis?

A Type I error is committed when

Which of the following would be an appropriate null hypothesis?

You know that the probability of committing a Type II error (β) is 5%, you can tell that the power of the test is

If a test of hypothesis has a Type I error probability (α) of 0.01, it means that

You know that the level of significance ( $\alpha$ ) of a test is 5%, you can tell that the probability of committing a Type II error ( $\beta$ ) is

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.

For a given sample size n, if the level of significance ( $\alpha$ ) is decreased, the power of the test

If an economist wishes to determine whether there is evidence that mean family income in a community equals $50,000

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

For a given level of significance, if the sample size is increased but the summary statistics remain the same, the probability of committing a Type I error will increase.

Quiz 9: Fundamentals of Hypothesis Testing: One-Sample Tests

If a researcher rejects a true null hypothesis, she has made a _______error.

The power of a test is measured by its capability of

If an economist wishes to determine whether there is evidence that mean family income in a community exceeds $50,000

If a researcher does not reject a true null hypothesis, she has made a _______decision.

For a given level of significance ( α\alphaα ) , if the sample size n is increased, the probability of a Type II error ( β\betaβ )

Which of the following would be an appropriate null hypothesis?

A Type II error is committed when

If the p-value is less than α in a two-tail test,

Which of the following would be an appropriate alternative hypothesis?

Which of the following would be an appropriate alternative hypothesis?

A Type I error is committed when

Which of the following would be an appropriate null hypothesis?

You know that the probability of committing a Type II error (β) is 5%, you can tell that the power of the test is

If a test of hypothesis has a Type I error probability (α) of 0.01, it means that

You know that the level of significance ( α\alphaα ) of a test is 5%, you can tell that the probability of committing a Type II error ( β\betaβ ) is

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.

For a given sample size n, if the level of significance ( α\alphaα ) is decreased, the power of the test

If an economist wishes to determine whether there is evidence that mean family income in a community equals $50,000

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

For a given level of significance, if the sample size is increased but the summary statistics remain the same, the probability of committing a Type I error will increase.

For a given level of significance ( $\alpha$ ) , if the sample size n is increased, the probability of a Type II error ( $\beta$ )

You know that the level of significance ( $\alpha$ ) of a test is 5%, you can tell that the probability of committing a Type II error ( $\beta$ ) is

For a given sample size n, if the level of significance ( $\alpha$ ) is decreased, the power of the test