Question 1

Although the null hypothesis may be implausible, it is never impossible.

Accepted Answer

The null hypothesis is a statement or assumption that there is no significant difference between two variables or sets of data. While it may be implausible, based on prior research or knowledge, it is never impossible, as it cannot be completely disproven. It is just simply not supported by the evidence or data being analyzed.

Question 2

The probability of committing a Type I error is the p value.

Accepted Answer

The p value is the probability of obtaining a result as extreme or more extreme than the observed results if the null hypothesis is true. It is not the probability of committing a Type I error, which is the probability of rejecting the null hypothesis when it is actually true. However, a smaller p value does indicate stronger evidence against the null hypothesis and therefore increases the risk of committing a Type I error if the significance level is not properly chosen.

Question 3

Our risk of a Type II error increases the most when:
A)Our sample size decreases, and we select a lower significance level (such as .01).
B)Our sample size increases, and we select a higher significance level (such as .10).
C)Our sample size decreases, and we select a higher significance level (such as .10).
D)Our sample size increases, and we select a lower significance level (such as .01).

Accepted Answer

A Type II error occurs when we fail to reject a false null hypothesis. Decreasing the sample size reduces the power of the test, making it harder to detect a true effect. Selecting a lower significance level (e.g., .01) makes the criteria for rejecting the null hypothesis more stringent, further increasing the risk of a Type II error.

Question 4

Every time we opt not to reject the null hypothesis, we inescapably risk making a Type II error.

Accepted Answer

When we fail to reject the null hypothesis, we may have made a correct decision, but there is still a chance that we have made a Type II error (i.e. incorrectly accepting a false null hypothesis). Therefore, there is always a risk of making a Type II error when we do not reject the null hypothesis.

Question 5

An experiment with a small sample is conducted to test the effectiveness of a promising new intervention for treating substance abuse.The experimental group's outcome is better than the control group's outcome, but the results are not statistically significant.The implication of this finding for evidence-based practice is:
A)The new intervention was ineffective.
B)The new intervention was effective, but not as effective as predicted.
C)It is conceivable that the new intervention is effective, although we cannot rule out sampling error as the explanation for the research finding.Additional testing of this intervention with a larger sample size would be in order.
D)None of these.

Accepted Answer

The fact that the experimental group had a better outcome than the control group suggests that the new intervention may be effective. However, the lack of statistical significance means that it is possible that the difference in outcomes could be due to chance (sampling error). Therefore, further testing with a larger sample size would be necessary to determine the efficacy of the new intervention. Option A, stating that the new intervention was ineffective, is not necessarily true based on the information given. Option B, stating that the new intervention was effective but not as effective as predicted, is speculative and not supported by the information given.

Question 6

We are least susceptible to committing Type II errors when our sample is small.

Accepted Answer

The statement is false. When our sample is small, we are more susceptible to committing Type II errors because there is less statistical power to detect a true difference between the groups being compared.

Question 7

The p-value resulting from a test of the statistical significance of a finding indicates:
A)The importance of the finding.
B)The actual strength of the predicted relationship.
C)The probability that the study's finding is attributable to sampling error.
D)The alpha level.

Accepted Answer

The p-value represents the probability that the observed effect was due to chance or sampling error. A low p-value (e.g., less than 0.05) indicates that there is strong evidence against the null hypothesis and that the finding is unlikely to be due to chance. Therefore, option C is the correct answer. Option A is incorrect because the p-value does not indicate the importance of the finding, only the likelihood that it is real. Option B is incorrect because the p-value does not indicate the strength of the relationship, only the likelihood that it is not due to chance. Option D is incorrect because the alpha level is predetermined and does not depend on the p-value.

Question 8

We commit a Type II error when we:
A)Reject a true null hypothesis.
B)Fail to reject a false null hypothesis.
C)Fail to reject a false research hypothesis.
D)Reject a false null hypothesis

Accepted Answer

A Type II error occurs when we fail to reject a false null hypothesis. This means that we have failed to detect a difference or association that exists in reality.

Question 9

We commit a Type I error when we:
A)Reject a true null hypothesis.
B)Fail to reject a false null hypothesis.
C)Reject a true research hypothesis.
D)Fail to reject a false research hypothesis.

Accepted Answer

A Type I error occurs when we reject a null hypothesis that is actually true. This means that we have wrongly concluded that there is a significant effect or relationship when in fact there is not. The probability of committing a Type I error is denoted by alpha, which is usually set at 0.05 or 0.01 in hypothesis testing.

Question 10

Which of the following statements is/are correct about p-values and significance levels?
A)If the p-value is .04, and the significance level is .05, then the result is statistically significant.
B)If the p-value is .05, and the significance level is .04, then the result is statistically significant.
C)If the p-value is .051, and the significance level is .05, then the result is statistically significant.
D)All of these.

Accepted Answer

A p-value of .04 is less than the significance level of .05, therefore the result is statistically significant. For B, the significance level should always be larger than the p-value in order for the result to be statistically significant. For C, the p-value is slightly larger than the significance level, therefore the result is not statistically significant.

Question 11

We risk a Type I error when we;
A)Reject the null hypothesis.
B)Fail to reject the null hypothesis.
C)Obtain results that are NOT statistically significant.
D)Reject a true research hypothesis.

Accepted Answer

Rejecting the null hypothesis means concluding that there is a significant effect or difference, but in reality, there may not be any. This means we have committed a Type I error.

Question 12

Which of the following statements is true about Type I and Type II errors?
A)Type I errors are always more serious.
B)Type II errors are always more serious.
C)Type I and Type II errors are always equally serious.
D)Which error is more serious will vary from study to study depending on the value judgments that we make.

Accepted Answer

The seriousness of Type I and Type II errors will vary depending on the context of the study and the value judgments that we make. In some situations, making a Type I error (false positive) could lead to serious consequences, such as a patient unnecessarily undergoing a risky medical procedure. In other situations, making a Type II error (false negative) could be more serious, such as a disease going undetected and untreated. Therefore, it is important to consider the specific circumstances of a study when determining which type of error is more serious.

Question 13

Which of the following statements is true about risking a Type II error?
A)We risk it when we reject the null hypothesis.
B)We risk it when we fail to reject the null hypothesis.
C)The same decision as to whether or not to reject a null hypothesis can risk a Type I and Type II error simultaneously.
D)None of these.

Accepted Answer

A Type II error occurs when we fail to reject the null hypothesis even though it is false. Therefore, choosing not to reject the null hypothesis increases the risk of making a Type II error.

Question 14

The most appropriate significance level in evidence-based practice research:
A)Should always be .05.
B)Should always be .10.
C)Is determined by mathematical theory.
D)Can vary, depending upon the sample size and judgments about the relative seriousness of Type I and Type II errors.

Accepted Answer

The most appropriate significance level in evidence-based practice research can vary, depending upon the sample size and judgments about the relative seriousness of Type I and Type II errors. A significance level of .05 or .10 is not always appropriate and is determined by statistical theory, not mathematical theory.

Question 15

Statistical conclusion validity:
A)Is based on the quality of data collection methods.
B)Is based on the strength of the logic of the research design.
C)Can be found in a study that lacks internal validity.
D)Requires that the relationship be strong.

Accepted Answer

Statistical conclusion validity refers to the degree to which conclusions about the relationship among variables based on the data are correct or reasonable. It can be present even if a study lacks internal validity, which is about the causal relationship between variables.

Question 16

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

Accepted Answer

A Type II error occurs when we fail to reject a false null hypothesis, meaning we accept a false conclusion.

Question 17

When our results are statistically significant, we refuse to reject the null hypothesis.

Accepted Answer

When our results are statistically significant, we reject the null hypothesis. This is because statistical significance indicates that the probability of obtaining our results by chance alone is extremely low, and therefore our results are likely due to a true effect or relationship. Rejecting the null hypothesis means we accept the alternative hypothesis as true.

Question 18

If the statewide re-arrest rate for drinking and driving is 40% and we predict that recipients of a new intervention to prevent recidivism will have a 10% recidivism rate, then:
A)the mean of the theoretical sampling distribution of the null hypothesis will be 40%.
B)the mean of the theoretical sampling distribution of the research hypothesis will be 10%.
C)the mean of the theoretical sampling distribution of the research hypothesis will be 30%.
D)the mean of the theoretical sampling distribution of the null hypothesis will be 30%.

Accepted Answer

The answer of If the statewide re-arrest rate for drinking...

Question 19

The Type II error probability is the proportion of the predicted sampling distribution that falls within the significant tail of the null hypothesis sampling distribution.

Accepted Answer

The definition given for the Type II error probability is incorrect. The correct definition is: The Type II error probability is the proportion of the null hypothesis sampling distribution that falls within the non-significant tail of the alternative hypothesis sampling distribution.

Question 20

A Type I error occurs whenever we reject a true null hypothesis.

Accepted Answer

A Type I error, also known as a false positive, occurs when we reject a null hypothesis that is actually true.

Quiz 12: Type I and Type Ii Errors

Although the null hypothesis may be implausible, it is never impossible.

The probability of committing a Type I error is the p value.

Our risk of a Type II error increases the most when:

Every time we opt not to reject the null hypothesis, we inescapably risk making a Type II error.

We are least susceptible to committing Type II errors when our sample is small.

The p-value resulting from a test of the statistical significance of a finding indicates:

We commit a Type II error when we:

We commit a Type I error when we:

Which of the following statements is/are correct about p-values and significance levels?

We risk a Type I error when we;

Which of the following statements is true about Type I and Type II errors?

Which of the following statements is true about risking a Type II error?

The most appropriate significance level in evidence-based practice research:

Statistical conclusion validity:

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

When our results are statistically significant, we refuse to reject the null hypothesis.

If the statewide re-arrest rate for drinking and driving is 40% and we predict that recipients of a new intervention to prevent recidivism will have a 10% recidivism rate, then:

The Type II error probability is the proportion of the predicted sampling distribution that falls within the significant tail of the null hypothesis sampling distribution.

A Type I error occurs whenever we reject a true null hypothesis.