Question 1

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?

Accepted Answer

The answer of A treatment is administered to a sample...

Question 2

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 critical z-values for a two-tailed test are approximately ±1.96 for α = .05 and ±2.58 for α = .01. A z-score of 2.37 falls beyond the critical value for α = .05 but not for α = .01, so the null hypothesis should be rejected at α = .05 but not at α = .01.

Question 3

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?

Accepted Answer

To reject the null hypothesis, we need to have a sample mean that is statistically significant, which means it is unlikely to occur by chance. This is determined by calculating the z-score and comparing it to the critical value based on the level of significance (α) and the standard deviation (σ). A higher standard deviation (σ) makes it harder to reject the null hypothesis, while a higher level of significance (α) makes it easier. Option B has a standard deviation of 5, which is less than option C, making it easier to reject the null hypothesis. Option B also has a level of significance of α = .05, which is less strict than option A, making it easier to reject the null hypothesis. Therefore, option B is the best choice.

Question 4

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?

Accepted Answer

The critical z-scores for a two-tailed test with α = 0.05 are approximately ±1.96. Since -2.24 is beyond -1.96, we reject the null hypothesis, indicating the treatment has an effect.

Question 5

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

The z-score of -1.90 does not fall beyond the critical boundaries of +1.96 and -1.96, so we fail to reject the null hypothesis (H0).

Question 6

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 is greater than 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 7

When is there a risk of a Type II error?

Accepted Answer

A Type II error occurs when the null hypothesis (H0) is not rejected when it is actually false. This risk is present whenever the decision is to "fail to reject H0".

Question 8

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?

Accepted Answer

Since the treatment is expected to increase the scores, the alternative hypothesis would be μ > 80. However, since we are conducting a one-tailed test, we need to choose the null hypothesis that complements the alternative hypothesis. Therefore, the null hypothesis would be μ ≤ 80, indicating that the treatment has no effect or may even decrease the scores. Option D is the correct statement of the null hypothesis.

Question 9

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

Accepted Answer

A very small treatment effect can still be significant if the sample size is very large because a larger sample size increases the power of a statistical test, making it easier to detect small effects.

Question 10

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?

Accepted Answer

A sample mean much different than 80 with α = .05 is more likely to reject the null hypothesis because the difference from the population mean suggests a treatment effect, and a higher alpha level (.05) makes it easier to reject the null hypothesis compared to .01.

Question 11

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?

Accepted Answer

The power of a test is the probability of correctly rejecting a false null hypothesis, which is 1 minus the probability of a Type II error (β). Therefore, if the power is 0.70, the probability of a Type II error is 0.30.

Question 12

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

Accepted Answer

Increasing the sample size will increase the power of the statistical test. This is because larger sample sizes provide more information and decrease the probability of random error, which ultimately increases the test's sensitivity and ability to detect true effects. Changing α or the type of test may affect the significance level, but it does not necessarily increase the power of the test.

Question 13

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?

Accepted Answer

For a one-tailed test with $\alpha$ = .01, the critical region is in the upper tail. The critical z-value for $\alpha$ = .01 in a one-tailed test is approximately 2.33.

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, then the sample mean should be similar to the population mean of 80. Therefore, the sample mean should be close to 80 and should lead to a failure to reject the null hypothesis.

Question 15

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?

Accepted Answer

Cohen's d measures the standardized effect size between two means. It is calculated by taking the difference between the means and dividing it by the standard deviation. 
d = (M - μ) / σ
d = (63 - 60) / 6
d = 0.50
Therefore, the value of Cohen's d for this sample is 0.50.

Question 16

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?

Accepted Answer

The larger sample size will increase the power of the hypothesis test and make it more likely to reject the null hypothesis, even with a relatively small standard deviation. A larger standard deviation would also make it easier to reject the null hypothesis, but the effect of sample size is larger in this case.

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?

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 large sample size increases the power of the test, making it easier to detect a significant effect.

Question 18

If a treatment has a very small effect, then what is a likely outcome for a hypothesis test evaluating the treatment?

Accepted Answer

A Type II error is likely when the treatment effect is very small, as it may not be detected, leading to a failure to reject the null hypothesis when it is actually false.

Question 19

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?

Accepted Answer

The critical value for a one-tailed test with α = .05 is approximately +1.645, and for α = .01, it is approximately +2.33. Since +1.85 is greater than +1.645 but less than +2.33, the null hypothesis can be rejected at α = .05 but not at α = .01.

Question 20

Which of the following is an accurate definition for the power of a statistical test?

Accepted Answer

The power of a statistical test is the probability of correctly rejecting a false null hypothesis. It measures the test's ability to detect an effect when there is one.

Quiz 8: Introduction to Hypothesis Testing

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 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 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?

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 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?

When is there a risk of a Type II error?

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

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?

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?

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

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\alphaα = .01, then which of the following correctly identifies the critical region?

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 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 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?

If a treatment has a very small effect, then what is a likely outcome for a hypothesis test evaluating the treatment?

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?

Which of the following is an accurate definition for the power of a statistical test?

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?