Deck 8: Introduction to Hypothesis Testing

Question 1

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

Answer 1

C

Question 2

Increasing the alpha level (for example from α = .01 to α = .05) _____.

A)increases the probability of a Type I error
B)increases the size of the critical region
C)increases the probability that the sample will fall into the critical region
D)All of the other options are results of increasing alpha.

Answer 2

D

Question 3

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.

Answer 3

A

Question 4

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

A)the average 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 5

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 6

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 7

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

Question 8

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 above

Question 9

If α is held constant at .05, what is the relationship between sample size, the critical region, and the risk of a Type I error?

A)As sample size increases, the critical region expands and the risk of a Type I error increases.
B)As sample size increases, the critical region shrinks and the risk of a Type I error increases.
C)As sample size increases, the critical region expands and the risk of a Type I error decreases.
D)There is no relationship between sample size, the critical region, and the risk of a Type I error.

Question 10

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 11

Which combination of factors will increase the chances of rejecting the null hypothesis?

A)a large standard error and a large alpha level
B)a large standard error and a small alpha level
C)a small standard error and a large alpha level
D)a small standard error and a small alpha level

Question 12

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 13

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 14

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 15

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 16

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

Question 17

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 18

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 19

Even if a treatment has an effect it is still possible to obtain a sample mean 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 20

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

A)the average 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 21

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 22

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 23

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 24

A two-tailed hypothesis test is being used to evaluate a treatment effect with ? = .05.If the sample data produce a z-score of z = -2.24, then 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 25

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, then what is the correct statistical decision?

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

Question 26

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 = 2.37.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 27

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 28

A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population which 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 > 80
B)μ > 80
C)μ < 80
D)μ < 80

Question 29

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

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

Question 30

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 31

If a hypothesis test is found to have power = 0.70, then 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 be determined without more information.

Question 32

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 33

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 $\alpha$ = .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 34

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 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.

Question 35

A sample of n = 16 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)2.00
D)3.00

Question 36

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 37

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 38

If a treatment has a very small effect, then 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 39

A researcher expects a treatment to produce an increase in the population mean.The treatment is evaluated using a one tailed hypothesis test, and the test produces z = +1.85.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 40

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 41

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 42

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

Question 43

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

Question 44

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

Question 45

If a research report includes the term significant result, it means that the null hypothesis was rejected.

Question 46

Most researchers would like the hypothesis test to reject the null hypothesis.

Question 47

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

Question 48

A research report includes the statement, z = 2.13, p < .05.For this hypothesis test, the used null hypothesis is rejected using an alpha level of α = .05.

Question 49

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

Question 50

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

Question 51

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

Question 52

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

Question 53

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 54

A researcher administers a treatment to a sample from a population with a mean of $\mu$ = 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 states that $\mu$ $\geq$ 60.

Question 55

The null hypothesis is stated in terms of the population, even though the data come from a sample.

Question 56

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 57

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

Question 58

A Type I 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 59

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

Question 60

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

Question 61

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 62

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 63

If other factors are held constant, the larger the size of the treatment effect, the greater the power of the hypothesis test.

Question 64

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

Question 65

A significant treatment effect does not necessarily indicate a large treatment effect.

Question 66

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 67

The power of a hypothesis test is the probability that the sample mean will be in the critical region if the treatment has an effect.

Question 68

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

Question 69

In a hypothesis test, the value obtained for the z-score is independent of the sample size.