Chapter 8
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. T or F?
False
If the sample data are in the critical region with a = .01, then the same sample data would still be in the critical region if a were changed to .05. T or F?
True
In a research report, p < .05 indicates that the probability of a Type I error is less than .05. T or F?
True
In a research report, the term significant result means that the null hypothesis was rejected. T or F?
True
In general, the null hypothesis states that the treatment has no effect on the population mean. T or F?
True
In most situations, researchers would like the hypothesis test to reject the null hypothesis. T or F?
True
It is possible for a very small treatment effect to be a statistically significant treatment effect. T or F?
True
The alpha level determines the risk of a Type I error. T or F?
True
The critical region for a hypothesis test consists of sample outcomes that are very unlikely to occur if the null hypothesis is true. T or F?
True
The null hypothesis predicts a specific value for the population mean. T or F?
True
The value obtained for Cohen's d is independent of the sample size. T or F?
True
There is always a possibility that the decision reached in a hypothesis test is incorrect. T or F?
True
A Type II error occurs when a researcher concludes that a treatment has an effect but, in fact, the treatment has no effect. T or F?
False
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. True or False?
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. T or F?
False
If a hypothesis test leads to rejecting the null hypothesis, it means that the sample data failed to provide sufficient evidence to conclude that the treatment has an effect. T or F?
False
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". T or F?
False
If other factors are held constant, lowering the alpha level will increase the power of a hypothesis test. T or F?
False
If the sample data are in the critical region with a = .05, then the same sample data would still be in the critical region if a were changed to .01. T or F?
False
The null hypothesis states that the sample mean (after treatment) is equal to the original population mean (before treatment). T or F?
False
You can reduce the risk of a Type I error by using a larger sample. T or F?
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
Which of the following is an accurate definition of a Type II error?
a) rejecting a false null hypothesis b) rejecting a true null hypothesis c) failing to reject a false null hypothesis* d) failing to reject a true null hypothesis
A researcher selects a sample and administers a treatment to the individuals in the sample. If the sample is used for a hypothesis test, what does the null hypothesis (Ho) say about the treatment?
a) the treatment causes a change in the scores b) the treatment adds a constant to each score c) the treatment multiplies each score by a constant d) the treatment has no effect on the scores*
When is there a risk of a Type I error?
a) whenever Ho is rejected* b) whenever H1 is rejected c) whenever the decision is "fail to reject Ho" d) the risk of a Type I error is independent of the decision from a hypothesis test
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. T or F?
True
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. T or F?
True
A Type I error occurs when a treatment has no effect but the decision is to reject the null hypothesis. T or F?
True
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. T or F?
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. T or F?
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. T or F?
True
If other factors are held constant, then increasing the sample size will increase the likelihood of rejecting the null hypothesis. T or F?
True
Which of the following accurately describes a hypothesis test?
a) a descriptive technique that allows researchers to describe a sample b) a descriptive technique that allows researchers to describe a population c) an inferential technique that uses the data from a sample to draw inferences about a population* d) an inferential technique that uses information about a population to make predictions about a sample
If a treatment has a very small effect, what is a likely outcome for a hypothesis test evaluating the treatment?
a) a type I error b) a type II error* c) correctly reject the null hypothesis d) correctly fail to reject the null hypothesis
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
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*
With a = .05, how are the boundaries for the critical region determined?
a) boundaries are drawn so there is 2.5% (.025) in each tail of the distribution* b) boundaries are drawn so there is 5% (.05) in each tail of the distribution c) boundaries are drawn so there is 10% (.10) in each tail of the distribution d) boundaries are drawn so there is 5% (.05) in the center of the distribution
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
What is the consequence of a Type I error?
a) concluding that a treatment has an effect when it really does b) concluding that a treatment has no effect when it really has no effect c) concluding that a treatment has no effect when it really does d) concluding that a treatment has an effect when it really has no effect*
What is the consequence of a Type II error?
a) concluding that a treatment has an effect when it really does b) concluding that a treatment has no effect when it really has no effect c) concluding that a treatment has no effect when it really does* d) concluding that a treatment has an effect when it really has no effect
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
For a hypothesis test evaluating the effect of a treatment on a population mean, what basic assumption is made concerning the treatment effect?
a) if there is a treatment effect, it will increase the scores b) if there is a treatment effect, it will decrease the scores c) if there is a treatment effect, it will add (or subtract) a constant to each score* d) if there is a treatment effect, it will multiply (or divide) each score by a constant
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
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
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 critical region?
a) outcomes with a very low probability if the null hypothesis is true* b) outcomes with a high probability if the null hypothesis is true c) outcomes with a very low probability whether or not the null hypothesis is true d) outcomes with a high probability whether or not the null hypothesis is true
If a hypothesis test produces a z-score in the critical region, what decision should be made?
a) reject the alternative hypothesis b) fail to reject the alternative hypothesis c) reject the null hypothesis* d) fail to reject the null hypothesis
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
Which of the following is an accurate definition of a Type I error?
a) rejecting a false null hypothesis b) rejecting a true null hypothesis* c) failing to reject a false null hypothesis d) failing to reject a true null hypothesis
A hypothesis test involves a comparison of which two elements?
a) research results from a sample and a hypothesis about a population* b) research results from a population and a hypothesis about a sample c) research results from a population and a hypothesis about the population d) research results from a sample and a hypothesis about the sample
Which of the following is directly addressed by the null hypothesis?
a) the population before treatment b) the population after treatment* c) the sample before treatment d) the sample after treatment
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
A sample of n = 25 individuals is selected from a population with u = 80, and a treatment is administered to the sample. What is the expected if the treatment has no effect?
a) the sample mean should be very different from 80 and should lead you to reject the null hypothesis b) the sample mean should be very different from 80 and should lead you to fail to reject the null hypothesis c) the sample mean should be close to 80 and should lead you to reject the null hypothesis d) the sample mean should be close 80 and should lead you to fail to reject the null hypothesis*
A researcher selects a sample and administers a treatment to the individuals in the sample. If the sample is used for a hypothesis test, what does the alternate hypothesis (H1) say about the treatment?
a) the treatment causes a change in the scores* b) the treatment adds a constant to each score c) the treatment multiplies each score by a constant d) the treatment has no effect on the scores
When is there a risk of a Type II error?
a) whenever Ho is rejected b) whenever H1 is rejected c) whenever the decision is "fail to reject Ho"* d) the risk of a Type II error is independent of the decision from a hypothesis 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. 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 less than 5%* 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 reject the null hypothesis. If the treatment actually does have an 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
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
