Question 1

Given the following values: $\mu$= 10,M = 8, $\sigma$_M = 0.5,conduct a one-sample z test at a .05 level of significance.What is the decision for a two-tailed test?

Accepted Answer

Since the significance level is .05, we need to find the critical values for a two-tailed test. Using a z-table, we find the critical values to be -1.96 and 1.96. We calculate the test statistic as:

z = (10 - 8) / (0.5 / sqrt(10)) = 4

Since the absolute value of the test statistic (|4|) is greater than the critical value of 1.96, we reject the null hypothesis. Therefore, the decision for a two-tailed test is to reject the null hypothesis.

Question 2

A researcher obtains z = 2.04 for a one-sample z test.What is the decision for this test at a .05 level of significance?

Accepted Answer

In one-sample z test, the null hypothesis is rejected if the calculated value of z is greater than the critical value of z. At a 0.05 level of significance, the critical value of z is 1.96 for a two-tailed test. Since the calculated value of z is 2.04 which is greater than 1.96, we reject the null hypothesis. Therefore, the decision is to reject the null hypothesis.

Question 3

______ allows researchers to describe (1)how far mean scores have shifted in the population or (2)the percentage of variance that can be explained by a given variable.

Accepted Answer

Effect size allows researchers to quantify the magnitude of the differences between groups or the strength of relationships between variables. It provides a standardized measure of the size of an effect, which can be used to compare results across different studies.

Question 4

When a researcher decides to retain the null hypothesis because the rejection region was located in the wrong tail,this is called a

Accepted Answer

A Type III error occurs when a researcher incorrectly specifies the direction of the hypothesis test, leading to the rejection region being placed in the wrong tail of the distribution. This is not a standard term in all statistical texts but is used by some to describe this specific mistake.

Question 5

Based on the effect size conventions,d = 0.18 is a

Accepted Answer

Generally, an effect size of d = 0.2 is considered small, therefore a value of d = 0.18 would also be considered small. Keep in mind that effect size conventions may vary slightly between fields of study.

Question 6

Based on the effect size conventions,d = 0.90 is a

Accepted Answer

Based on the effect size conventions, a d = 0.90 is considered a large effect size. This indicates that the difference between groups is significant and meaningful.

Question 7

A researcher obtains z = 1.45 for a one-sample z test.What is the decision for this test at a .05 level of significance?

Accepted Answer

The answer of A researcher obtains z = 1.45 for...

Question 8

The power of the decision-making process is

Accepted Answer

The power of the decision-making process in statistical hypothesis testing is the likelihood of correctly rejecting a false null hypothesis. This means it measures the test's ability to detect an effect if there is one.

Question 9

Given the following values: $\mu$ = 6.0,M = 7.6,n = 36, $\sigma$ = 6,conduct a one-sample z test at a .05 level of significance.For a one-tailed test,upper-tail critical,what is the decision?

Accepted Answer

The answer of Given the following values: $\mu$ = 6.0,M...

Question 10

A researcher obtains z = 3.98 for a one-sample z test.If her decision is to retain the null hypothesis,then what do you know about her decision?

Accepted Answer

The answer of A researcher obtains z = 3.98 for...

Question 11

Based on the effect size conventions,d = 0.60 is a

Accepted Answer

Based on the effect size conventions, d = 0.60 is considered a medium effect size. This means there is a significant difference between groups, but it is not considered a large effect.

Question 12

A professor finds that the average SAT score among all students attending his college is 1150 ± 150 ($\mu$±  $\sigma$).He polls his class of 25 students and finds that the average SAT score is 1200.Suppose he computes a one-sample z test at a .05 level of significance.What is his decision?

Accepted Answer

The answer of A professor finds that the average SAT...

Question 13

A researcher obtains z = -6.45.What is the decision for a one-tailed test,upper-tail critical,at a .05 level of significance?

Accepted Answer

In a one-tailed test, specifically an upper-tail test, a negative z-score (like -6.45) indicates that the sample mean is significantly lower than the population mean hypothesized under the null hypothesis. However, since we're looking at the upper tail, we're interested in whether the sample mean is significantly higher, not lower. Therefore, a negative z-score does not lead to rejecting the null hypothesis at the .05 level of significance in an upper-tail test. We retain the null hypothesis because the evidence does not support a significantly higher mean than hypothesized.

Question 14

A researcher reports that the size of an effect in Population A is d = 0.10 and the effect size in Population B is d = 0.34.Which population is associated with greater power to detect an effect?

Accepted Answer

The effect size in Population B is larger than the effect size in Population A, which means that Population B is associated with greater power to detect an effect. Larger effect sizes are generally easier to detect and require smaller sample sizes to achieve a given level of power.

Question 15

A researcher obtains z = 1.80 for a one-sample z test.What is the decision for this test at a .05 level of significance?

Accepted Answer

The decision to reject or retain the null hypothesis at a .05 level of significance depends on whether the test is one-tailed or two-tailed, as the critical z-value changes accordingly.

Question 16

A measure of the size of an effect in a population is called

Accepted Answer

Effect size measures the magnitude of a phenomenon or the extent of the relationship between two variables in a population. It is different from significance, which simply determines the likelihood of an observed effect occurring by chance, and from probability, which describes the chance of a certain event happening. Power refers to the ability of a statistical test to detect a true effect, but it does not provide information about the size of the effect. Therefore, the best answer is D - effect size.

Question 17

The probability of committing a Type I error is stated by ______; the probability of committing a Type II error is stated by ______.

Accepted Answer

The probability of committing a Type I error (rejecting a true null hypothesis) is stated by alpha, while the probability of committing a Type II error (failing to reject a false null hypothesis) is stated by beta. Option A is reversed, option C is incomplete as the p value represents the probability of obtaining a test statistic as extreme as the one observed assuming the null hypothesis is true, and option D mentions power, which is the complement of beta and represents the probability of correctly rejecting a false null hypothesis.

Question 18

A researcher reports that the size of an effect in some population is d = 0.88.Which of the following is an appropriate interpretation for d?

Accepted Answer

The effect size (d = 0.88) represents the standardized mean difference between two groups or conditions. Specifically, it indicates that the mean scores on the outcome variable shifted by 0.88 standard deviations in the population, which is a moderately large effect size. Therefore, option D is the appropriate interpretation. Option A suggests significance, but d alone does not provide information about statistical significance. Option B refers to mean scores in the sample, not the population, and option C repeats this error and suggests significance without providing necessary statistical tests.

Question 19

A researcher selects a sample of 36 students from a school population with a mean IQ of 100 and a standard deviation of 12.She determines that the mean IQ in this sample is 104.Assuming she computes a one-sample z test at a .05 level of significance,what is the decision for a two-tailed test?

Accepted Answer

To determine the decision for the one-sample z test, we need to calculate the z-score:

z = (sample mean - population mean) / (standard deviation / square root of sample size)
z = (104 - 100) / (12 / sqrt(36))
z = 2

Since this is a two-tailed test, we need to look up the critical z-value at the .025 level of significance, which is 1.96 (using a z-table or calculator).

Since our calculated z-value of 2 is greater than the critical z-value of 1.96, we reject the null hypothesis. This means that there is evidence to suggest that the mean IQ score in the sample is significantly higher than the mean IQ score in the population.

Question 20

The one-sample z test is a hypothesis test used to test hypotheses

Accepted Answer

The one-sample z test is specifically used to test hypotheses about a single population with a known variance. It compares a sample mean to a population mean, where the population standard deviation is already known.

Quiz 8: Hypothesis Testing: Significance,effect Size,and Power

Given the following values: $\mu$ = 10,M = 8, $\sigma$ _M = 0.5,conduct a one-sample z test at a .05 level of significance.What is the decision for a two-tailed test?

A researcher obtains z = 2.04 for a one-sample z test.What is the decision for this test at a .05 level of significance?

______ allows researchers to describe (1) how far mean scores have shifted in the population or (2) the percentage of variance that can be explained by a given variable.

When a researcher decides to retain the null hypothesis because the rejection region was located in the wrong tail,this is called a

Based on the effect size conventions,d = 0.18 is a

Based on the effect size conventions,d = 0.90 is a

A researcher obtains z = 1.45 for a one-sample z test.What is the decision for this test at a .05 level of significance?

The power of the decision-making process is

Given the following values: $\mu$ = 6.0,M = 7.6,n = 36, $\sigma$ = 6,conduct a one-sample z test at a .05 level of significance.For a one-tailed test,upper-tail critical,what is the decision?

A researcher obtains z = 3.98 for a one-sample z test.If her decision is to retain the null hypothesis,then what do you know about her decision?

Based on the effect size conventions,d = 0.60 is a

A professor finds that the average SAT score among all students attending his college is 1150 ± 150 ( $\mu$ ± $\sigma$ ) .He polls his class of 25 students and finds that the average SAT score is 1200.Suppose he computes a one-sample z test at a .05 level of significance.What is his decision?

A researcher obtains z = -6.45.What is the decision for a one-tailed test,upper-tail critical,at a .05 level of significance?

A researcher reports that the size of an effect in Population A is d = 0.10 and the effect size in Population B is d = 0.34.Which population is associated with greater power to detect an effect?

A researcher obtains z = 1.80 for a one-sample z test.What is the decision for this test at a .05 level of significance?

A measure of the size of an effect in a population is called

The probability of committing a Type I error is stated by ; the probability of committing a Type II error is stated by .

A researcher reports that the size of an effect in some population is d = 0.88.Which of the following is an appropriate interpretation for d?

A researcher selects a sample of 36 students from a school population with a mean IQ of 100 and a standard deviation of 12.She determines that the mean IQ in this sample is 104.Assuming she computes a one-sample z test at a .05 level of significance,what is the decision for a two-tailed test?

The one-sample z test is a hypothesis test used to test hypotheses

Quiz 8: Hypothesis Testing: Significance,effect Size,and Power

Given the following values: μ\muμ = 10,M = 8, σ\sigmaσ M = 0.5,conduct a one-sample z test at a .05 level of significance.What is the decision for a two-tailed test?

A researcher obtains z = 2.04 for a one-sample z test.What is the decision for this test at a .05 level of significance?

______ allows researchers to describe (1) how far mean scores have shifted in the population or (2) the percentage of variance that can be explained by a given variable.

When a researcher decides to retain the null hypothesis because the rejection region was located in the wrong tail,this is called a

Based on the effect size conventions,d = 0.18 is a

Based on the effect size conventions,d = 0.90 is a

A researcher obtains z = 1.45 for a one-sample z test.What is the decision for this test at a .05 level of significance?

The power of the decision-making process is

Given the following values: μ\muμ = 6.0,M = 7.6,n = 36, σ\sigmaσ = 6,conduct a one-sample z test at a .05 level of significance.For a one-tailed test,upper-tail critical,what is the decision?

A researcher obtains z = 3.98 for a one-sample z test.If her decision is to retain the null hypothesis,then what do you know about her decision?

Based on the effect size conventions,d = 0.60 is a

A professor finds that the average SAT score among all students attending his college is 1150 ± 150 ( μ\muμ ± σ\sigmaσ ) .He polls his class of 25 students and finds that the average SAT score is 1200.Suppose he computes a one-sample z test at a .05 level of significance.What is his decision?

A researcher obtains z = -6.45.What is the decision for a one-tailed test,upper-tail critical,at a .05 level of significance?

A researcher reports that the size of an effect in Population A is d = 0.10 and the effect size in Population B is d = 0.34.Which population is associated with greater power to detect an effect?

A researcher obtains z = 1.80 for a one-sample z test.What is the decision for this test at a .05 level of significance?

A measure of the size of an effect in a population is called

The probability of committing a Type I error is stated by ______; the probability of committing a Type II error is stated by ______.

A researcher reports that the size of an effect in some population is d = 0.88.Which of the following is an appropriate interpretation for d?

A researcher selects a sample of 36 students from a school population with a mean IQ of 100 and a standard deviation of 12.She determines that the mean IQ in this sample is 104.Assuming she computes a one-sample z test at a .05 level of significance,what is the decision for a two-tailed test?

The one-sample z test is a hypothesis test used to test hypotheses

Given the following values: $\mu$ = 10,M = 8, $\sigma$ _M = 0.5,conduct a one-sample z test at a .05 level of significance.What is the decision for a two-tailed test?

Given the following values: $\mu$ = 6.0,M = 7.6,n = 36, $\sigma$ = 6,conduct a one-sample z test at a .05 level of significance.For a one-tailed test,upper-tail critical,what is the decision?

A professor finds that the average SAT score among all students attending his college is 1150 ± 150 ( $\mu$ ± $\sigma$ ) .He polls his class of 25 students and finds that the average SAT score is 1200.Suppose he computes a one-sample z test at a .05 level of significance.What is his decision?

The probability of committing a Type I error is stated by ; the probability of committing a Type II error is stated by .