Question 1

Which of the following represents the probability of a Type II error?​

Accepted Answer

Probability of a Type II error is denoted by β.

Question 2

If α is held constant at .05,what is the impact of changing the sample size on the critical region and the risk of a Type I error?​

Accepted Answer

The critical region and the risk of a Type I error are determined by the significance level (α), not the sample size. Therefore, if α is held constant, changes in sample size do not affect the critical region or the risk of a Type I error.

Question 3

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

Accepted Answer

Increasing the alpha level from .01 to .05 means that the researcher is willing to accept a higher level of Type I error risk (the risk of rejecting a null hypothesis that is actually true). Therefore, increasing the alpha level would increase the likelihood of rejecting H₀ and increase the risk of a Type I error.

Question 4

Decreasing the alpha level from α = .05 to α = .01 ____.​

Accepted Answer

Decreasing the alpha level from .05 to .01 means we are decreasing the probability of rejecting the null hypothesis when it is actually true. This means that we are decreasing the probability of a Type I error.  Therefore, the correct answer is D.

Question 5

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?​

Accepted Answer

The z-score of 2.37 corresponds to a p-value of approximately 0.018, which is less than both α = .05 and α = .01. Therefore, the researcher should reject the null hypothesis at α = .05, but not necessarily at α = .01.

Question 6

Which of the following accurately describes the critical region?​

Accepted Answer

The critical region is defined as the set of outcomes that have a very low probability of occurring if the null hypothesis is true. This is the region where the null hypothesis is rejected in favor of the alternative hypothesis.

Question 7

Which of the following is an accurate definition of a Type II error?​​

Accepted Answer

A Type II error occurs when the null hypothesis is false, but the statistical analysis fails to reject it. This means that the error is in not identifying an effect or difference that actually exists.

Question 8

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,then what is the correct decision?​

Accepted Answer

The correct decision is to reject the null hypothesis and conclude that the treatment has an effect since the z-score of 2.24 exceeds the critical value of ±1.96 at α = .05 for a two-tailed test.

Question 9

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

Accepted Answer

The numerator of the z-score test statistic measures the actual distance between the sample mean (M) and the population mean (µ) in terms of standard errors. It is calculated by subtracting µ from M and dividing the result by the standard error of the mean (SEM). This value is then compared to the critical z-value to determine if the difference between M and µ is statistically significant.

Question 10

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

Accepted Answer

The alpha level determines the probability of rejecting the null hypothesis when it is actually true. The critical region is the area in the sampling distribution where the null hypothesis is rejected. As the alpha level increases, the critical region becomes larger, making it easier to reject the null hypothesis. However, this also increases the risk of a Type I error, or falsely rejecting the null hypothesis when it is actually true. Therefore, increasing the alpha level increases the size of the critical region and the risk of a Type I error.

Question 11

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?​

Accepted Answer

A z-score of 2.37 exceeds the critical value for a one-tailed test at both α = .05 (z = 1.645) and α = .01 (z = 2.33), so the null hypothesis is rejected at both significance levels.

Question 12

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?​

Accepted Answer

Rejecting the null hypothesis when it is actually true (due to an extreme sample mean) results in a Type I error.

Question 13

Which of the following accurately describes a hypothesis test?​

Accepted Answer

A hypothesis test is an inferential technique that uses the data from a sample to draw inferences about a population. It involves testing a specific hypothesis about the population based on the information obtained from the sample. This allows researchers to make conclusions about the population based on the results obtained from the sample.

Question 14

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?​

Accepted Answer

If the treatment has no effect, we would expect the sample mean to be close to the population mean of 80. Therefore, the best choice is D, which states that the sample mean should be close to 80 and should lead you to fail to reject the null hypothesis (which assumes the treatment has no effect). If the sample mean is very different from 80, it would suggest that the treatment has an effect and would lead to rejecting the null hypothesis.

Question 15

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

Accepted Answer

The denominator of the z-score test statistic measures the standard error of the mean, which represents the average distance between the sample mean (M) and the population mean (µ) that would be expected if the null hypothesis were true. This standard error is used to standardize the difference between the sample mean and the population mean, allowing for comparison across different scales.

Question 16

Which of the following is directly addressed by the null hypothesis?​

Accepted Answer

The answer of Which of the following is directly addressed...

Question 17

By selecting a larger alpha level,a researcher is ____.​

Accepted Answer

Selecting a larger alpha level increases the probability of rejecting the null hypothesis even if it is true, which increases the risk of a Type I error. Therefore, the statement that best describes this situation is C, increasing the risk of a Type I error.

Question 18

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?

Accepted Answer

Since the z-score of 1.90 falls between -1.96 and +1.96, we fail to reject the null hypothesis H₀ at a significance level of 0.05. Therefore, we do not have enough evidence to conclude that the alternative hypothesis H₁ is true.

Question 19

Which of the following is an accurate definition of a Type I error?​

Accepted Answer

A Type I error occurs when we reject a true null hypothesis, meaning we conclude that there is evidence to support an effect or relationship when there really isn't one. This is also known as a false positive result.

Question 20

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?​

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.

Quiz 8: Introduction to Hypothesis Testing

Which of the following represents the probability of a Type II error?

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

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

Decreasing the alpha level from α = .05 to α = .01 ____.

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 critical region?

Which of the following is an accurate definition of a Type II error?

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,then what is the correct decision?

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

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 = 2.37.If the researcher is using a one-tailed test,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?

Which of the following accurately describes a hypothesis test?

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?

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

Which of the following is directly addressed by the null hypothesis?

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

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?

Which of the following is an accurate definition of a Type I error?

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?

Quiz 8: Introduction to Hypothesis Testing

Which of the following represents the probability of a Type II error?​

If α is held constant at .05,what is the impact of changing the sample size on the critical region and the risk of a Type I error?​

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

Decreasing the alpha level from α = .05 to α = .01 ____.​

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 critical region?​

Which of the following is an accurate definition of a Type II error?​​

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,then what is the correct decision?​

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

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 = 2.37.If the researcher is using a one-tailed test,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?​

Which of the following accurately describes a hypothesis test?​

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?​

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

Which of the following is directly addressed by the null hypothesis?​

By selecting a larger alpha level,a researcher is ____.​

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?

Which of the following is an accurate definition of a Type I error?​

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?​

Which of the following represents the probability of a Type II error?

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

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

Decreasing the alpha level from α = .05 to α = .01 ____.

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 critical region?

Which of the following is an accurate definition of a Type II error?

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,then what is the correct decision?

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

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 = 2.37.If the researcher is using a one-tailed test,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?

Which of the following accurately describes a hypothesis test?

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?

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

Which of the following is directly addressed by the null hypothesis?

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

Which of the following is an accurate definition of a Type I error?

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?