Question 1

You complete a hypothesis test using $\alpha$ = .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.

Accepted Answer

Rejecting the null hypothesis when it is actually true is a Type I error. The significance level of the hypothesis test (α = .05) indicates that there is a 5% chance of making a Type I error. Therefore, if the null hypothesis is true, there is a possibility of having made a Type I error by rejecting it.

Question 2

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

Accepted Answer

Increasing the sample size decreases the standard error because as the sample size increases, the sample mean becomes a better estimate of the population mean. It does not affect the risk of a Type I error, which is determined by the significance level (alpha) and the test statistic.

Question 3

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

Accepted Answer

If a treatment has an effect but the sample mean is very similar to the original population mean, it is likely that the null hypothesis (H0) will not be rejected when it should be. This scenario leads to a Type II error, where the failure to reject the null hypothesis occurs despite there being a true effect.

Question 4

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.

Accepted Answer

The alpha level is the level of significance chosen by the researcher, which determines the probability of making a Type I error. The critical region is the area in the distribution of the test statistic that represents extreme values that are unlikely to occur by chance. As the alpha level increases, the critical region becomes larger, making it more likely that a statistically significant result will be obtained by chance (i.e., the risk of a Type I error increases).

Question 5

You complete a hypothesis test using $\alpha$= .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.

Accepted Answer

If the treatment actually does have an effect and you reject the null hypothesis, you have made the correct decision.

Question 6

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

Accepted Answer

The critical boundaries for a hypothesis test are used to determine whether to reject or fail to reject the null hypothesis. In this case, the null hypothesis is not given, but we can assume it to be H0: μ = μ0 (a two-sided test). The critical z-value for this test at a 5% level of significance is ±1.96. The critical F-value is given by F1F1F1S1F1F1F101.96, which is not relevant to this question. The z-score for the sample data is z = 1.90, which is between the critical boundaries of ±1.96. Therefore, we fail to reject the null hypothesis and conclude that there is not enough evidence to say that the sample mean is significantly different from the hypothesized mean at a 5% level of significance. The correct choice is B, "Fail to reject H₀."

Question 7

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

Accepted Answer

Since the z-score is 2.27, which corresponds to a p-value of approximately .0115, the decision will depend on the chosen level of significance. For a one-tailed test with α = .05, the critical value is 1.645. Since 2.27 > 1.645, we can reject the null hypothesis. However, for a one-tailed test with α = .01, the critical value is 2.33. Since 2.27 < 2.33, we cannot reject the null hypothesis. Therefore, the correct decision is to reject the null hypothesis with α = .05 but not with α = .01.

Question 8

You complete a hypothesis test using $\alpha$= .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.

Accepted Answer

Failing to reject the null hypothesis when the treatment actually does have an effect is a Type II error.

Question 9

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

Accepted Answer

The correct decision is to reject the null hypothesis and conclude that the treatment has an effect. This is because the calculated z-score of 102.24 is greater than the critical values of ±1.96 for a two-tailed hypothesis test with α = .05. This means that the probability of obtaining such an extreme result under the null hypothesis is very low, and we can reject the null hypothesis in favor of the alternative hypothesis that the treatment has an effect.

Question 10

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

Accepted Answer

If an extreme sample mean is obtained that is very different from the population mean, there is a risk of rejecting the null hypothesis even if it is true (Type I error). Therefore, the best choice is A – reject H₀ and make a Type I error.

Question 11

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.

Accepted Answer

Selecting a larger alpha level increases the likelihood of rejecting the null hypothesis (H0), makes it easier to detect a treatment effect, and increases the risk of a Type I error, which is rejecting a true null hypothesis.

Question 12

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

Accepted Answer

A larger standard deviation (σ) makes it harder to find significant differences, and a higher alpha level (α) makes it easier to reject the null hypothesis. Therefore, a smaller σ (5) and a higher α (.05) increase the likelihood of rejecting the null hypothesis.

Question 13

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

Accepted Answer

Increasing the alpha level increases the risk of a Type I error (false positive), which means rejecting the null hypothesis when it is actually true. This does not have any effect on the standard error, which is a measure of how much variability there is in the sample data.

Question 14

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

Accepted Answer

A z-score of 2.37 corresponds to a p-value of approximately .018, which is less than both α = .05 and α = .01. Therefore, the researcher should reject the null hypothesis with α = .05 but not necessarily with α = .01.

Question 15

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.

Accepted Answer

Decreasing the alpha level reduces the probability of making a Type I error (rejecting a true null hypothesis), which in turn decreases the size of the critical region (the range of values for which the null hypothesis is rejected). Consequently, this also reduces the likelihood that a given sample will fall into this critical region, making all the options correct outcomes of lowering the alpha level.

Question 16

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

Accepted Answer

Increasing the alpha level increases the cutoff point for statistical significance, making it easier to reject the null hypothesis. However, this also increases the risk of a Type I error (rejecting the null hypothesis when it is actually true).

Question 17

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

Accepted Answer

A sample mean significantly different from the population mean (µ = 80) with a higher alpha level (α = .05) increases the likelihood of rejecting the null hypothesis because it indicates a more substantial effect of the treatment and a higher tolerance for Type I error.

Question 18

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

Accepted Answer

A sample mean much different than 80 for a large sample is most likely to result in rejecting the null hypothesis because a larger sample size increases the power of the test to detect significant differences from the population mean. Additionally, a sample mean that is much different than 80 means that there is less overlap between the sample distribution and the population distribution, making it more likely that the difference is statistically significant.

Question 19

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

Accepted Answer

A larger sample size (n = 50) and a smaller standard deviation (σ = 5) will result in a larger t-value and a smaller p-value, making it more likely to reject the null hypothesis.

Question 20

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 > 80 B)μ > 80. C)μ < 80 D)μ < 80,

Accepted Answer

The null hypothesis always assumes that there is no significant difference, so in this case, the null hypothesis would be that the treatment does not increase the scores, resulting in a population mean of μ = 80. Therefore, option D (μ < 80) is the correct statement of the null hypothesis. Option A is incorrect because it assumes that the population mean is already very low, which is not given in the problem. Option B is incorrect because it assumes that the treatment is already effective before conducting the experiment. Option C is incorrect because it assumes that the population mean is already high, which is again, not given in the problem.

Quiz 8: Introduction to Hypothesis Testing

You complete a hypothesis test using $\alpha$ = .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?

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

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?

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

You complete a hypothesis test using $\alpha$ = .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?

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 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?

You complete a hypothesis test using $\alpha$ = .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 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?

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?

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

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?

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

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?

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

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

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 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 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?

Quiz 8: Introduction to Hypothesis Testing

You complete a hypothesis test using α\alphaα = .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?

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

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?

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

You complete a hypothesis test using α\alphaα = .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?

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 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?

You complete a hypothesis test using α\alphaα = .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 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?

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?

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

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?

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

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?

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

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

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 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 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?

You complete a hypothesis test using $\alpha$ = .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?

You complete a hypothesis test using $\alpha$ = .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?

You complete a hypothesis test using $\alpha$ = .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?