Question 1

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 is the probability of correctly rejecting a false null hypothesis. Option C states this definition correctly. Option A is incorrect because rejecting a null hypothesis that is actually true is a Type I error. Option B is incorrect because not rejecting a null hypothesis that is actually false is a Type II error. Option D is incorrect because a false null hypothesis should be rejected to make the correct decision.

Question 2

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

B

Question 3

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

Accepted Answer

Type I

Question 4

If the Type I error (α) for a given test is to be decreased, then for a fixed sample size n
A) the Type II error (β) will also decrease.
B) the Type II error (β) will increase.
C) the power of the test will increase.
D) a one-tail test must be utilized.

Accepted Answer

The answer of If the Type I error (α) for...

Question 5

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 no less than 0.65.
D) The sample proportion is no less than 0.65.

Accepted Answer

The alternative hypothesis should state what the researcher is trying to prove or find evidence for. In this case, option A is the appropriate alternative hypothesis because it states that the population proportion is less than 0.65, which would be evidence against the null hypothesis that the population proportion is equal to or greater than 0.65. Option B does not work as the alternative hypothesis because it only refers to the sample proportion, not the population proportion. Option C is incorrect because it is not stating anything that can be tested or proven through the statistical analysis. Option D is similar to option B and does not refer to the population proportion.

Question 6

If a researcher accepts a false null hypothesis, she has made a ________ error.

Accepted Answer

The answer of If a researcher accepts a false null...

Question 7

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 no less than 0.65.
D) The sample proportion is no less than 0.65.

Accepted Answer

The null hypothesis should always assume that there is no difference or effect. In this case, the null hypothesis should state that the population proportion is no less than 0.65, as this assumes that there is no significant difference from the hypothesized value. The sample proportion may have variation, so it is not a suitable null hypothesis.

Question 8

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

Accepted Answer

Type I error is the probability of rejecting a true null hypothesis. Therefore, if the α level is 0.01, we reject the null hypothesis when the probability of the observed result occurring by chance is less than 1% (0.01). Hence, if the null hypothesis is true, we reject it 1% of the time.

Question 9

If a researcher rejects a false null hypothesis, she has made a ________ decision.

Accepted Answer

The answer of If a researcher rejects a false null...

Question 10

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

Accepted Answer

The level of significance (α) and the probability of committing a Type II error (β) are not directly related. Therefore, knowing α does not allow us to determine β.

Question 11

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

The null hypothesis should always include an equality statement, such as "equal to," "not equal to," or "less than or equal to/greater than or equal to." Option A fits this criteria as it states that the mean of the population is equal to a specific value. Option B is incorrect because it refers to a sample rather than a population. Option C is incorrect because it includes a directional statement, which should be included in the alternative hypothesis instead. Option D is incorrect because option C is not an appropriate null hypothesis.

Question 12

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

Accepted Answer

As the level of significance is decreased, the critical region for rejecting the null hypothesis becomes smaller. This means it is less likely to reject the null hypothesis, leading to a decrease in power (the ability to correctly reject the null hypothesis when it is false).

Question 13

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 to determine if there is evidence that the mean family income in a community equals $50,000 because we are testing for whether the mean is significantly different from $50,000, regardless of whether it is higher or lower. A one-tail test would only be appropriate if we had a specific directional hypothesis, such as wanting to test whether the mean family income is significantly higher than $50,000.

Question 14

If a researcher accepts a true null hypothesis, she has made a ________ decision.

Accepted Answer

The answer of If a researcher accepts a true null...

Question 15

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 16

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

The alternative hypothesis should state what the researcher is trying to prove or find evidence for. In this case, the researcher is proposing that the mean of the population is greater than 55, which is a statement that can be tested and supported by data. Options A and B are null hypotheses, stating equality, which cannot be tested directly. Option D is not appropriate because it refers to a sample mean rather than the population mean, which is the focus of the hypothesis test.

Question 17

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

Accepted Answer

As the sample size n increases, the standard error decreases, which in turn leads to a greater likelihood of rejecting the null hypothesis if it is truly false (i.e. a true positive result) and a lower likelihood of accepting the null hypothesis if it is truly false (i.e. a false negative or Type II error). Therefore, increasing the sample size reduces the probability of a Type II error.

Question 18

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

Accepted Answer

A Type II error occurs when we fail to reject a null hypothesis that is actually false.

Question 19

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

Accepted Answer

A Type I error occurs when we reject a null hypothesis that is true, meaning we conclude there is an effect or difference when there actually is not.

Question 20

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

If the p-value is less than α in a two-tail test, it means that the observed result is statistically significant and the probability of obtaining such a result due to chance is low. Therefore, the null hypothesis should be rejected, and the alternative hypothesis should be accepted.

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

The power of a test is measured by its capability of

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 researcher rejects a true null hypothesis, she has made a ________ error.

If the Type I error (α) for a given test is to be decreased, then for a fixed sample size n

Which of the following would be an appropriate alternative hypothesis?

If a researcher accepts a false null hypothesis, she has made a ________ error.

Which of the following would be an appropriate null hypothesis?

If a test of hypothesis has a Type I error probability (α) of 0.01, we mean

If a researcher rejects a false null hypothesis, she has made a ________ decision.

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

Which of the following would be an appropriate null hypothesis?

For a given sample size n, if the level of significance (α) 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

If a researcher accepts a true null hypothesis, she has made a ________ decision.

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

Which of the following would be an appropriate alternative hypothesis?

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

A Type II error is committed when

A Type I error is committed when

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