### The Probability, Type I Error, Type II Error, Hypothesis Test, Alpha Level – Statistical Test

The key terms in these Statistics chapters include Hypothesis Test, Type I Error, The Probability, Type II Error, Decreases The Probability, Alpha Level, Null Hypothesis, Sample Size, Reject The Null Hypothesis, Critical Region, Standard Error, Two-tailed Hypothesis, Statistical Test.

You complete a hypothesis test using a = .05, and based on the evidence from the sample, your decision is to reject the null hypothesis. If the treatment actually has no effect, which of the following is true?

**a) you have made a type I error**

b) you have made a type II error

c) you might have made a type I error, but the probability is only 5% at most

d) you have made the correct decision

You complete a hypothesis test using a = .05, and based on the evidence from the sample, your decision is to fail to reject the null hypothesis. If the treatment actually has no effect, which of the following is true?

a) you have made a type I error**b) you have made a type II error**

c) you might have made a type I error, but the probability is only 5% at most

d) you have made the correct decision

A set of scores ranges from a high of X = 63 to a low of X = 28. If these scores were put in a grouped frequency distribution table, what would be the best choice for the interval width?

**5 Points**

What is the relationship between the alpha level, the size of the critical region, and the risk of a Type I error?

**a) as the alpha level increases, the size of the critical region increases, and the risk of a Type I error increases**

b) as the alpha level increases, the size of the critical region increases, and the risk of a Type I error decreases

c) as the alpha level increases, the size of the critical region decreases, and the risk of Type I error increases

d) as the alpha level increases, the size of the critical region decreases, and the risk of a Type I error decreases

A Type I error occurs when a treatment has no effect but the decision is to reject the null hypothesis.

**True**

Which of the following correctly describes the effect of increasing the alpha level (for example, from .01 to .05)?

**a) increase the likelihood of rejecting Ho and increase the risk of a Type I error**

b) decrease the likelihood of rejecting Ho and increase the risk of a Type I error

c) increase the likelihood of rejecting Ho and decrease the risk of a Type I error

d) decrease the likelihood of rejecting Ho and decrease the risk of a Type I error

By selecting a larger alpha level, a researcher is ________.

a) attempting to make it easier to reject Ho

b) better able to detect a treatment effect

c) increasing the risk of a type I error**d) all of the other options are the results of selecting a larger alpha level**

A Type I error occurs when a treatment has no effect but the decision is to reject the null hypothesis.

**True**

What is the effect of decreasing the alpha level (for example, from a = .05 to a = .01)?

a) it decreases the probability of a type I error

b) it decreases the size of the critical region

c) it decreases the probability that the sample will fall into the critical region**d) all of the other options are results of decreasing alpha**

Which of the following accurately describes the effect of increasing the sample size?

a) increases the standard error and has no effect on the risk of a type I error**b) decreases the standard error and has no effect on the risk of a type I error**

c) increases the risk of a type I error and has no effect on the standard error

d) decreases the risk of a type I error and has no effect on the standard error

Which of the following accurately describes the effect of increasing the alpha level?

a) increases the standard error and has no effect on the risk of a type I error

b) decreases the standard error and has no effect on the risk of a type I error**c) increases the risk of a type I error and has no effect on the standard error**

d) decreases the risk of a type I error and has no effect on the standard error

A Type I error occurs when a treatment has no effect but the decision is to reject the null hypothesis.

**True**

You complete a hypothesis test using a = .05, and based on the evidence from the sample, your decision is to reject the null hypothesis. If the treatment actually has no effect, which of the following is true?

**a) you have made a type I error**

b) you have made a type II error

c) you might have made a type I error, but the probability is only 5% at most

d) you have made the correct decision

You complete a hypothesis test using a = .05, and based on the evidence from the sample, your decision is to fail to reject the null hypothesis. If the treatment actually has no effect, which of the following is true?

a) you have made a type I error**b) you have made a type II error**

c) you might have made a type I error, but the probability is only 5% at most

d) you have made the correct decision

What is the relationship between the alpha level, the size of the critical region, and the risk of a Type I error?

**a) as the alpha level increases, the size of the critical region increases, and the risk of a Type I error increases**

b) as the alpha level increases, the size of the critical region increases, and the risk of a Type I error decreases

c) as the alpha level increases, the size of the critical region decreases, and the risk of Type I error increases

d) as the alpha level increases, the size of the critical region decreases, and the risk of a Type I error decreases

If individuals are pressured into participating in research because the researcher is in a position of power or authority, then which ethical principle is being compromised?

**Informed consent**

Which of the following correctly describes the effect of increasing the alpha level (for example, from .01 to .05)?

**a) increase the likelihood of rejecting Ho and increase the risk of a Type I error**

b) decrease the likelihood of rejecting Ho and increase the risk of a Type I error

c) increase the likelihood of rejecting Ho and decrease the risk of a Type I error

d) decrease the likelihood of rejecting Ho and decrease the risk of a Type I error

By selecting a larger alpha level, a researcher is ________.

a) attempting to make it easier to reject Ho

b) better able to detect a treatment effect

c) increasing the risk of a type I error**d) all of the other options are the results of selecting a larger alpha level**

A Type II error occurs when a researcher concludes that a treatment has an effect but, in fact, the treatment has no effect.

**False**

A Type II error occurs when a treatment actually does have an effect on the scores but the effect was not large enough to reject the null hypothesis.

**True**

The alpha level determines the risk of a Type I error.

**True**

You can reduce the risk of a Type I error by using a larger sample.

**True**

There is always a possibility that the decision reached in a hypothesis test is incorrect.

**True**

A two-tailed hypothesis is being used to evaluate a treatment effect with a = .05. If the sample data produce a z-score of z = -2.24, what is the correct decision?

a) reject the null hypothesis and conclude that the treatment has no effect**b) reject the null hypothesis and conclude that the treatment has an effect**

c) fail to reject the null hypothesis and conclude that the treatment has no effect

d) fail to reject the null hypothesis and conclude that the treatment has an effect

If a hypothesis test rejects the null hypothesis using an alpha level of a = .05, then the research report would include the statement, “p > .05”.

**False**

In a research report, p < .05 indicates that the probability of a Type I error is less than .05.

**True**

In a research report, the term significant result means that the null hypothesis was rejected.

**True**

If other factors are held constant, then increasing the sample size will increase the likelihood of rejecting the null hypothesis.

**True**

Which of the following is an accurate definition for the power of a statistical test?

a) the probability of rejecting a true null hypothesis

b) the probability of supporting true null hypothesis**c) the probability of rejecting a false null hypothesis**

d) the probability of supporting a false null hypothesis

Which of the following will increase the power of a statistical test?

a) change a from .05 to .01

b) change from a one-tailed test to a two-tailed test**c) change the sample size from n = 25 to n = 100**

d) none of the other options will increase power

The power of a hypothesis test is the probability that the sample mean will be in the critical region even if the treatment has no effect.

**False**

If the power for a hypothesis test is calculated to be 0.80, then for same test, the probability of a Type II error is 0.20.

**True**

If all other factors are held constant, increasing the sample size from n = 25 to n = 100 will increase the power of a statistical test.

**True**

If other factors are held constant, lowering the alpha level will increase the power of a hypothesis test.

**False**

A researcher evaluates a treatment effect using a two-tailed hypothesis test with a = .05, and the decision is to reject the null hypothesis. If the researcher switched to a one-tailed test using the same sample, what decision would be made?

**a) definitely reject the null hypothesis with a = .05 and maybe reject with a = .01**

b) definitely reject the null hypothesis with a = .05 and with a = .01

c) definitely fail to reject the null hypothesis with either a = .05 or with a = .01

d) it is impossible to predict the outcome of the one-tailed test

A researcher evaluates a treatment effect using a one-tailed hypothesis test with a = .05, and the decision is to reject the null hypothesis. If the researcher switched to a two-tailed test using the same sample, what decision would be made?

a) definitely reject the null hypothesis with either a = .05 or with a = .01

b) definitely reject the null hypothesis with a = .05 and maybe reject with a = .01**c) might reject the null hypothesis with a = .05 but might not**

d) definitely fail to reject the null hypothesis with either a = .05 or with a = .01

If the research prediction is that the treatment will decrease scores, then the critical region for a directional test will be in the left-hand tail.

**True**

A researcher administers a treatment to a sample from a population with a mean of u = 60. If the treatment is expected to increase scores and a one-tailed test is used to evaluate the treatment effect, then the null hypothesis would state that u >/= 60.

**False**

A researcher is evaluating a treatment that is expected to increase scores. If a one-tailed test with a = .05 is used, then the critical region consists of z-scores less than -1.65.

**False**

The value obtained for Cohen’s d is independent of the sample size.

**True**

It is possible for a very small treatment effect to be a statistically significant treatment effect.

**True**

Although the size of the sample can influence the outcome of a hypothesis test, it has little or no influence on measures of effect size.

**True**

Which of the following is an accurate definition for the power of a statistical test?

a) the probability of rejecting a true null hypothesis

b) the probability of supporting true null hypothesis**c) the probability of rejecting a false null hypothesis**

d) the probability of supporting a false null hypothesis

Which of the following will increase the power of a statistical test?

a) change a from .05 to .01

b) change from a one-tailed test to a two-tailed test**c) change the sample size from n = 25 to n = 100**

d) none of the other options will increase power

The power of a hypothesis test is the probability that the sample mean will be in the critical region even if the treatment has no effect.

**False**

If the power for a hypothesis test is calculated to be 0.80, then for same test, the probability of a Type II error is 0.20.

**True**

If all other factors are held constant, increasing the sample size from n = 25 to n = 100 will increase the power of a statistical test.

**True**

If other factors are held constant, lowering the alpha level will increase the power of a hypothesis test.

**False**

A Type II error occurs when a researcher concludes that a treatment has an effect but, in fact, the treatment has no effect.

**False**

A Type II error occurs when a treatment actually does have an effect on the scores but the effect was not large enough to reject the null hypothesis.

**True**

The alpha level determines the risk of a Type I error.

**True**

You can reduce the risk of a Type I error by using a larger sample.

**True**

There is always a possibility that the decision reached in a hypothesis test is incorrect.

**True**

A two-tailed hypothesis is being used to evaluate a treatment effect with a = .05. If the sample data produce a z-score of z = -2.24, what is the correct decision?

a) reject the null hypothesis and conclude that the treatment has no effect**b) reject the null hypothesis and conclude that the treatment has an effect**

c) fail to reject the null hypothesis and conclude that the treatment has no effect

d) fail to reject the null hypothesis and conclude that the treatment has an effect

If a hypothesis test rejects the null hypothesis using an alpha level of a = .05, then the research report would include the statement, “p > .05”.

**False**

If individuals are pressured into participating in research because the researcher is in a position of power or authority, then which ethical principle is being compromised?

**Informed consent**

Who is acting as a confederate?

**Jay, who pretends to be a research participant even though he is actually working with the experimenter**

The Milgram study involved ____.

**Asking participants to administer what appeared to be severe shocks to other people**

The Belmont Report provides basic ethical guidelines for the ____.

**Treatment of human participants in research**

A researcher who deliberately omits informing participants about the true intent of a questionnaire is committing ____.

**Passive deception**

One responsibility of the IACUC is to ensure that ____.

**Discomfort is minimized in nonhuman subjects in research**

Which example violates the ethical guidelines concerning deception?

**Administering shocks without giving participants advanced warning and obtaining consent**

In research with nonhuman subjects, researchers ________.

**Do not need to justify their research**

Passive deception refers to ____.

**Withholding information from participants**

What is one of the guidelines for using deception in a research study?

**The deception cannot conceal a real risk or danger to participants.**

A set of scores ranges from a high of X = 63 to a low of X = 28. If these scores were put in a grouped frequency distribution table, what would be the best choice for the interval width?

**5 Points**

A biologist records the number and types of fish caught in a local lake during a 2- year period. The biologist reports that 7% of the fish caught during this period were trout, whereas 43% of the fish caught were bass. These reports of the number of trout and bass at this lake are examples of _____.

**Relative frequencies**