Deck 8: Introduction to Hypothesis Testing.

Question 1

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

Answer 1

Failing to reject a false null hypothesis

Question 2

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 alternative 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.

Answer 2

The treatment causes a change in the scores.

Question 3

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

Answer 3

Outcomes with a very low probability if the null hypothesis is true

Question 4

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

Question 5

Withα= .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.

Question 6

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

Question 7

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.

Question 8

What is measured by the numerator of the z-score test statistic?

A)A likely distance between M and µ that would be expected if H0 was true
B)The actual distance between M and µ
C)The position of the sample mean relative to the critical region
D)Whether or not there is a significant difference between M and µ

Question 9

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

Question 10

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

Question 11

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

Question 12

When is there a risk of a Type I error?

A)Whenever H0 is rejected
B)Whenever H1 is rejected
C)Whenever the decision is "fail to reject H0"
D)The risk of a Type I error is independent of the decision from a hypothesis test.

Question 13

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 (H₀)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.

Question 14

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

Question 15

You complete a hypothesis test using α = .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.

Question 16

What is measured by the denominator of the z-score test statistic?

A)A likely distance between M and µ that would be expected if H0 was true
B)The actual distance between M and µ
C)The position of the sample mean relative to the critical region
D)Whether or not there is a significant difference between M and µ

Question 17

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

Question 18

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

Question 19

When is there a risk of a Type II error?

A)Whenever H0 is rejected
B)Whenever H1 is rejected
C)Whenever the decision is "fail to reject H0"
D)The risk of a Type II error is independent of the decision from a hypothesis test.

Question 20

A sample of n = 25 individuals is selected from a population with µ = 80,and a treatment is administered to the sample.What is expected if the treatment has no effect?

A)The sample mean after the treatment should be very different from 80 and should lead you to reject the null hypothesis.
B)The sample mean after the treatment should be very different from 80 and should lead you to fail to reject the null hypothesis.
C)The sample mean after the treatment should be close to 80 and should lead you to reject the null hypothesis.
D)The sample mean after the treatment should be close 80 and should lead you to fail to reject the null hypothesis.

Question 21

A two-tailed hypothesis test is being used to evaluate a treatment effect with α = .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

Question 22

Even if a treatment has an effect,it is still possible to obtain a sample mean after the treatment that is very similar to the original population mean.What outcome is likely if this happens?

A)Reject H0 and make a Type I error
B)Correctly reject H0
C)Fail to reject H0 and make a Type II error
D)Correctly fail to reject H0

Question 23

The critical boundaries for a hypothesis test are z = +1.96 and -1.96.If the z-score for the sample data is z = -1.90,what is the correct statistical decision?

A)Fail to reject H₁
B)Fail to reject H₀
C)Reject H₁
D)Reject H₀

Question 24

Even if a treatment has no effect,it is still possible to obtain an extreme sample mean that is very different from the population mean.What outcome is likely if this happens?

A)Reject H0 and make a Type I error
B)Correctly reject H0
C)Fail to reject H0 and make a Type II error
D)Correctly fail to reject H0

Question 25

A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population that is known to have a mean of μ = 80.The results will be examined using a one-tailed hypothesis test.Which of the following is the correct statement of the null hypothesis?

A)μ > 40
B)μ > 120
C)μ < 85
D)μ < 80

Question 26

A researcher administers a treatment to a sample of participants selected from a population with µ = 80.If a hypothesis test is used to evaluate the effect of the treatment,which combination of factors is most likely to result in rejecting the null hypothesis?

A)A sample mean near 80 for a small sample
B)A sample mean near 80 for a large sample
C)A sample mean much different than 80 for a small sample
D)A sample mean much different than 80 for a large sample

Question 27

What is the effect of decreasing the alpha level (for example,from α = .05 to α = .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.

Question 28

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 a 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.

Question 29

A researcher conducts a hypothesis test to evaluate the effect of a treatment that is expected to increase scores.The hypothesis test produces a z-score of z = 2.27.If the researcher is using a one-tailed test,what is the correct statistical decision?

A)Reject the null hypothesis with α = .05 but not with α = .01.
B)Reject the null hypothesis with either α = .05 or α = .01.
C)Fail to reject the null hypothesis with either α = .05 or α = .01.
D)Cannot answer without additional information

Question 30

A researcher administers a treatment to a sample of participants selected from a population with µ = 80.If the researcher obtains a sample mean of M = 88,which combination of factors is most likely to result in rejecting the null hypothesis?

A)σ = 5 and n = 25
B)σ = 5 and n = 50
C)σ = 10 and n = 25
D)σ = 10 and n = 50

Question 31

A researcher administers a treatment to a sample of participants selected from a population with µ = 80.If a hypothesis test is used to evaluate the effect of the treatment,which combination of factors is most likely to result in rejecting the null hypothesis?

A)A sample mean near 80 with α = .05
B)A sample mean near 80 with α = .01
C)A sample mean much different than 80 with α = .05
D)A sample mean much different than 80 with α = .01

Question 32

You complete a hypothesis test using α = .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.

Question 33

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

A)attempting to make it easier to reject H0
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 result of selecting a larger alpha level.

Question 34

You complete a hypothesis test using α = .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.

Question 35

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 H0 and increase the risk of a Type I error
B)Decrease the likelihood of rejecting H0 and increase the risk of a Type I error
C)Increase the likelihood of rejecting H0 and decrease the risk of a Type I error
D)Decrease the likelihood of rejecting H0 and decrease the risk of a Type I error

Question 36

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

Question 37

A researcher conducts a hypothesis test to evaluate the effect of a treatment.The hypothesis test produces a z-score of z = 2.37.Assuming that the researcher is using a two-tailed test,what decision should be made?

A)The researcher should reject the null hypothesis with α = .05 but not with α = .01.
B)The researcher should reject the null hypothesis with either α = .05 or α = .01.
C)The researcher should fail to reject H0 with either α = .05 or α = .01.
D)Cannot answer without additional information

Question 38

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

Question 39

You complete a hypothesis test using α = .05,and based on the evidence from the sample,your decision is to fail 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.

Question 40

A researcher administers a treatment to a sample of participants selected from a population with µ = 80.If the researcher obtains a sample mean of M = 88,which combination of factors is most likely to result in rejecting the null hypothesis?

A)σ = 5 and α = .01
B)σ = 5 and α = .05
C)σ = 10 and α = .01
D)σ = 10 and α = .05

Question 41

In most situations,researchers would like the hypothesis test to reject the null hypothesis.

Question 42

The null hypothesis states that the sample mean (after treatment)is equal to the original population mean (before treatment).

Question 43

A researcher expects a treatment to increase the scores for individuals in a population.The treatment is evaluated using a one-tailed hypothesis test,and the test produces z = +2.40.Based on this result,what is the correct statistical decision?

A)The researcher should reject the null hypothesis with α = .05 but not with α = .01.
B)The researcher should reject the null hypothesis with either α = .05 or α = .01.
C)The researcher should fail to reject H0 with either α = .05 or α = .01.
D)Cannot answer without additional information

Question 44

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.

Question 45

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

Question 46

The critical region for a hypothesis test consists of sample outcomes that are very unlikely to occur if the null hypothesis is true.

Question 47

In general,the null hypothesis states that the treatment has no effect on the population mean.

Question 48

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

A)Definitely reject the null hypothesis with α = .05 and maybe reject with α = .01
B)Definitely reject the null hypothesis with α = .05 and with α = .01
C)Definitely fail to reject the null hypothesis with either α = .05 or with α = .01
D)It is impossible to predict the outcome of the one-tailed test.

Question 49

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

Question 50

A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population.If the researcher uses a one-tailed test with α = .01,then which of the following correctly identifies the critical region?

A)z > 2.33
B)z > 2.58
C)z < 2.33
D)z < 2.58

Question 51

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

A)Change α 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.

Question 52

A treatment is administered to a sample of n = 9 individuals selected from a population with a mean of µ = 80 and a standard deviation of σ = 12.After treatment,the effect size is measured by computing Cohen's d,and a value of d = 0.50 is obtained.Based on this information,what is the mean for the treated sample?

A)M = 6
B)M = 82
C)M = 86
D)Cannot answer without knowing the sample size

Question 53

If the sample data are in the critical region with α = .05,then the same sample data would still be in the critical region if α were changed to .01.

Question 54

Under what circumstances can a very small treatment effect still be significant?

A)If the sample size (n) is very large
B)If the sample standard deviation (?) is very large
C)If the standard error of M (? _M) is very large
D)All of the other factors are likely to produce a significant result.

Question 55

A sample of n = 9 individuals is selected from a population with μ = 60 and σ = 6,and a treatment is administered to the sample.After treatment,the sample mean is M = 63.What is the value of Cohen's d for this sample?

A)0.33
B)0.50
C)1.00
D)2.00

Question 56

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

Question 57

A researcher evaluates a treatment effect using a one-tailed hypothesis test with α = .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 α = .05 or with α = .01
B)Definitely reject the null hypothesis with α = .05 and maybe reject with α = .01
C)Might reject the null hypothesis with α = .05 but might not
D)Definitely fail to reject the null hypothesis with either α = .05 or with α = .01

Question 58

If a hypothesis test is found to have power = 0.70,what is the probability that the test will result in a Type II error?

A)0.30
B)0.70
C)p > 0.70
D)Cannot determine without more information

Question 59

If the sample data are in the critical region with α = .01,then the same sample data would still be in the critical region if α were changed to .05.

Question 60

The null hypothesis predicts a specific value for the population mean.

Question 61

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

Question 62

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

Question 63

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

Question 64

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

Question 65

In a hypothesis test,the likelihood of rejecting the null hypothesis is independent of the sample size.

Question 66

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

Question 67

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

Question 68

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.

Question 69

A researcher administers a treatment to a sample of n = 16 selected from a population with µ = 40 and Ϭ = 8.If the sample mean after treatment is M = 42,then Cohen's d = 1.00.

Question 70

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.

Question 71

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

Question 72

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

Question 73

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

Question 74

A researcher administers a treatment to a sample from a population with a mean of µ = 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 µ ≥ 60.

Question 75

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.

Question 76

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.

Question 77

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.

Question 78

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

Question 79

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.

Question 80

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