Question 1

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

Since this is a two-tailed hypothesis test, the rejection region exists in both tails of the distribution, with a total area of α/2 = .025 in each tail. A z-score of -2.24 corresponds to a probability of .0127 in the left tail of the distribution, which is smaller than α/2. Therefore, we reject the null hypothesis and conclude that the treatment has an effect.

Question 2

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

Accepted Answer

If a treatment has an effect but the sample mean after the treatment is very similar to the original population mean, it is likely that the statistical test will not detect a significant difference. This scenario leads to failing to reject the null hypothesis (H0) when it is false, which is a Type II error.

Question 3

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 z-score for the sample data falls within the critical boundaries of z = +1.96 and -1.96, which are the boundaries for a 95% confidence level. Therefore, we fail to reject the null hypothesis (H0) and conclude that there is not enough evidence to support the alternative hypothesis (H1) at a 95% significance level.

Question 4

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

Even if the treatment has no effect, there is always a chance of obtaining an extreme sample mean just by chance. If this happens, and we reject the null hypothesis, we are making a Type I error (false positive). This is because we are concluding that the treatment had an effect, when in fact it did not.

Question 5

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

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.

Question 6

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 as a larger sample size increases the power of the test and increases the likelihood of detecting a true effect. A sample mean very different from the population mean of 80 would also indicate a stronger effect of the treatment.

Question 7

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 8

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 represents the probability of making a Type I error, which is rejecting a true null hypothesis. The critical region is the area in the tail(s) of the sampling distribution where we reject the null hypothesis. As the alpha level increases, we widen the critical region, which increases the probability of rejecting the null hypothesis when it is actually true, leading to a higher risk of a Type I error.

Question 9

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 it is a one-tailed test, the rejection region is only in one tail of the distribution. Therefore, we need to compare the z-score obtained with the critical value of the normal distribution at the corresponding alpha level. For alpha level of .05, the critical z-value is 1.645. For alpha level of .01, the critical z-value is 2.326. Since the obtained z-score (2.27) is greater than the critical z-value at alpha level of .05 but less than the critical z-value at alpha level of .01, we can reject the null hypothesis with alpha level of .05 but cannot reject it with alpha level of .01.

Question 10

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

The larger sample size (n = 50) reduces the standard error of the mean and increases the power to detect significant differences from the population mean. The smaller population standard deviation (σ = 5) also helps to increase power. Therefore, option B (σ = 5 and n = 50) is most likely to result in rejecting the null hypothesis.

Question 11

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 much different than 80 with α = .05 is most likely to result in rejecting the null hypothesis because a significant deviation from the population mean (µ = 80) increases the likelihood of rejecting the null hypothesis, and a higher alpha level (α = .05) means there is a less stringent criterion for significance compared to α = .01, making it easier to reject the null hypothesis.

Question 12

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.

Accepted Answer

Rejecting the null hypothesis when it is actually true (no effect) is a Type I error, which occurs when the significance level (α) is exceeded. In this case, the significance level was set to α = .05, meaning there is a 5% chance of making a Type I error. Therefore, it is possible that a Type I error was made in this situation.

Question 13

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 makes it easier to reject the null hypothesis (H0), increases the ability to detect a treatment effect, and also increases the risk of committing a Type I error (incorrectly rejecting a true null hypothesis). All these outcomes are interconnected consequences of choosing a larger alpha level.

Question 14

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.

Accepted Answer

Rejecting the null hypothesis when the treatment does have an effect means you have correctly identified that there is an effect, thus making the correct decision.

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

Accepted Answer

Increasing the alpha level increases the critical region and thus increases the likelihood of rejecting H0. However, it also increases the area in the tails of the distribution, which increases the risk of a Type I error (rejecting a true null hypothesis). So, increasing alpha level will increase the likelihood of rejecting H0 and increase the risk of a Type I error.

Question 16

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, which is rejecting the null hypothesis when it is actually true. This means that there is a higher probability of finding a significant effect when there is no true effect. However, increasing the alpha level does not affect the standard error, which is a measure of the variability of the sample means around the population mean.

Question 17

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. This means that if the null hypothesis is true, there is only a .018 probability of obtaining a z-score this extreme or more extreme in either direction. Since this is less than the chosen level of significance of .05, the researcher should reject the null hypothesis with α = .05. However, since .018 is greater than α = .01, the researcher should not reject the null hypothesis with α = .01. Therefore, the correct decision is to reject the null hypothesis with α = .05 but not with α = .01.

Question 18

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, as it increases the precision of the estimate. However, it has no effect on the risk of a Type I error, which is determined by the chosen significance level and the statistical test used.

Question 19

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.

Accepted Answer

Failing to reject the null hypothesis when the treatment actually has an effect indicates a Type II error, which occurs when the null hypothesis is incorrectly not rejected.

Question 20

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.

Quiz 8: Introduction to Hypothesis Testing.

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 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?

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?

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 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?

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

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

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 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 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?

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?

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

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?

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

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?

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

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 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?