Question 1

If α = .01 and p > .01 for a two-tailed independent samples t test, then we can conclude that

Accepted Answer

The p-value is greater than the alpha level, so we fail to reject the null hypothesis and conclude that there is no significant difference between the means.

Question 2

The mean stubbornness scores for the 8 individuals in sample A was 36. The mean for sample B, consisting of 12 individuals, was 42. A two-tailed independent samples t test was conducted and t_obt = +2.33. Given an α = .05, we can conclude that

Accepted Answer

A t-value of +2.33 with an α = .05 typically indicates a significant difference between the two groups, leading to the rejection of the null hypothesis. This means both B (there was a significant difference between the means) and C (the null hypothesis should be rejected) are correct.

Question 3

A two-tailed independent samples t test was conducted with an α = .01. The mean for group A, consisting of 8 individuals, was 63. The mean for group B, consisting of 9 individuals, was 61. If the obtained t-value was -2.63, we could conclude that

Accepted Answer

The answer of A two-tailed independent samples t test was...

Question 4

A psychologist has developed a workshop designed to increase the degree of optimism that people experience. She conducts a one-tailed independent samples t test with an α = .01 to determine if the workshop in fact improves optimism scores. Group A, consisting of 16 individuals, participated in the workshop and subsequently obtained a M₁ = 92 on an optimism assessment. Group B, consisting of 13 individuals, takes the assessment without attending the workshop and obtained a M₂ = 88. If the obtained t-value was +2.33, we could conclude that

Accepted Answer

The answer of A psychologist has developed a workshop designed...

Question 5

In a two-tailed independent samples t test, the null hypothesis specifies the difference between means values to be ________.

Accepted Answer

The null hypothesis in a two-tailed independent samples t test specifies that the difference between means values is zero.

Question 6

If SS for group one is 32 and SS for group two is 51 and both groups are made up of 7 individuals, what is  ?

Accepted Answer

To calculate the pooled variance (SP²), we first need to calculate the variance for each group by dividing the sum of squares (SS) by the degrees of freedom (df). The df for each group is the number of individuals (n) minus one (df = n-1).

For group one: variance = SS/df = 32/(7-1) = 4
For group two: variance = SS/df = 51/(7-1) = 8.5

Then, we can calculate the pooled variance by weighting the variances for each group by their degrees of freedom and adding them together, then dividing by the total degrees of freedom (n1 + n2 - 2).

SP² = ((n1-1)*variance1 + (n2-1)*variance2)/(n1+n2-2)
     = ((7-1)*4 + (7-1)*8.5)/(7+7-2)
     = 6.08

Therefore, the answer is C) 1.39, which is the square root of the pooled variance (SP), rounded to two decimal places.

Question 7

The difference between M₁ and M₂ is 12. The pooled variance is 5. Which of the following can be used to determine Cohen's d for an independent samples t test?

Accepted Answer

Cohen's d can be calculated using the formula d = (M1 - M2) / √((s1² + s2²) / 2), where M1 and M2 are the means of the two groups and s1² and s2² are the variances. Since the variances are equal in an independent samples t test, we can use the pooled variance (s²) instead of s1² and s2². Therefore, d = (M1 - M2) / √(s²/2). Plugging in the given values, we get d = 12 / √(5/2) = 12 / 2.236 = 5.36. Thus, the correct choice is B.

Question 8

The difference between means is 4. The pooled variance is 9. What is the value of Cohen's d for an independent samples t test?

Accepted Answer

Cohen's d formula for an independent samples t test is:
d = (X1 - X2) / sqrt(sp^2)
where X1 - X2 is the difference between means, sqrt is the square root, and sp^2 is the pooled variance.
 
Substituting the given values:
d = 4 / sqrt(9)
d = 4 / 3
d = 1.33
 
Therefore, the answer is D.

Question 9

The following results were reported for an independent samples t test: t(21) = -2.32, p > .01. The results suggest that

Accepted Answer

The p-value is reported as being greater than .01, which means that there is not enough evidence to reject the null hypothesis. Therefore, H₀ should fail to be rejected.

Question 10

The following results were reported for an independent samples t test: t(18) = +2.15, p < .05. The results suggest that

Accepted Answer

The t-test result of t(18) = +2.15 with a p-value less than .05 suggests that the observed data are unlikely under the null hypothesis (H₀), indicating statistically significant differences between the groups. Therefore, H₀ should be rejected (A), and the results are unlikely if H₀ is true (C), making both A and C correct.

Question 11

If our obtained t-value for an independent samples t test is -2.21 and we are using a nondirectional alternative hypothesis, which of the following t_crit value(s) will lead to the rejection of H₀?

Accepted Answer

For a nondirectional (two-tailed) hypothesis test, we compare the absolute value of our obtained t-value to the critical t-value(s). Since our obtained t-value is -2.21, we look at both the positive and negative critical values. Both +2.18 and -2.03, when considering their absolute values, are less than the absolute value of our obtained t-value (2.21), meaning our obtained t-value falls in the rejection region for either of these critical values.

Question 12

Given a t_crit of -2.01 for an independent samples t test, which of the following obtained t-value will lead to the rejection of H₀?

Accepted Answer

The obtained t-value must be less than the critical t-value in order to reject the null hypothesis. Therefore, any negative obtained t-value that is greater than -2.01 will lead to rejection of H₀. The only choice for a negative obtained t-value that is larger in absolute value than -2.01 is -2.33, therefore the answer is B.

Question 13

For an independent samples t test, the ________ the difference between the sample means, the ________ the likelihood of rejecting H₀.

Accepted Answer

For an independent samples t-test, the larger the difference between the sample means, the greater the likelihood of rejecting the null hypothesis (H₀), because a larger difference suggests a stronger effect or difference between the groups being compared.

Question 14

Which of the following is not one of the assumptions of the independent samples t test?

Accepted Answer

The assumption of homogeneity of variance applies to the dependent variable across groups defined by the independent variable, not to the independent variable itself. The independent variable is typically categorical in the context of an independent samples t-test.

Question 15

The homogeneity of variance assumption for the independent samples t test requires that

Accepted Answer

The homogeneity of variance assumption for the independent samples t test requires that the population variances of the dependent variable be approximately equal. The other options (B, C, and D) are irrelevant to the homogeneity of variance assumption.

Question 16

Explain the difference between a one-sample t test and an independent samples t test.

Accepted Answer

The answer of Explain the difference between a one-sample t...

Question 17

Using symbolic notation, write the null and alternative hypotheses for a two-tailed independent samples t test.

Accepted Answer

The answer of Using symbolic notation, write the null and...

Question 18

Using symbolic notation, write the null and alternative hypotheses for a one-tailed independent samples t test for which the researcher expects the scores in condition one to be higher than the scores in condition two.

Accepted Answer

The answer of Using symbolic notation, write the null and...

Question 19

Using symbolic notation, write the null and alternative hypotheses for a one-tailed independent samples t test for which the researcher expects the scores in condition one to be lower than the scores in condition two.

Accepted Answer

The answer of Using symbolic notation, write the null and...

Question 20

Describe in words what the null and alternative hypotheses state for a two-tailed independent samples t test.

Accepted Answer

The answer of Describe in words what the null and...

Quiz 10: Two-Sample T-Test: Independent Samples Design

If α = .01 and p > .01 for a two-tailed independent samples t test, then we can conclude that

The mean stubbornness scores for the 8 individuals in sample A was 36. The mean for sample B, consisting of 12 individuals, was 42. A two-tailed independent samples t test was conducted and t_obt = +2.33. Given an α = .05, we can conclude that

A two-tailed independent samples t test was conducted with an α = .01. The mean for group A, consisting of 8 individuals, was 63. The mean for group B, consisting of 9 individuals, was 61. If the obtained t-value was -2.63, we could conclude that

In a two-tailed independent samples t test, the null hypothesis specifies the difference between means values to be ________.

If SS for group one is 32 and SS for group two is 51 and both groups are made up of 7 individuals, what is ?

The difference between M₁ and M₂ is 12. The pooled variance is 5. Which of the following can be used to determine Cohen's d for an independent samples t test?

The difference between means is 4. The pooled variance is 9. What is the value of Cohen's d for an independent samples t test?

The following results were reported for an independent samples t test: t(21) = -2.32, p > .01. The results suggest that

The following results were reported for an independent samples t test: t(18) = +2.15, p < .05. The results suggest that

If our obtained t-value for an independent samples t test is -2.21 and we are using a nondirectional alternative hypothesis, which of the following t_crit value(s) will lead to the rejection of H₀?

Given a t_crit of -2.01 for an independent samples t test, which of the following obtained t-value will lead to the rejection of H₀?

For an independent samples t test, the the difference between the sample means, the the likelihood of rejecting H₀.

Which of the following is not one of the assumptions of the independent samples t test?

The homogeneity of variance assumption for the independent samples t test requires that

Explain the difference between a one-sample t test and an independent samples t test.

Using symbolic notation, write the null and alternative hypotheses for a two-tailed independent samples t test.

Using symbolic notation, write the null and alternative hypotheses for a one-tailed independent samples t test for which the researcher expects the scores in condition one to be higher than the scores in condition two.

Using symbolic notation, write the null and alternative hypotheses for a one-tailed independent samples t test for which the researcher expects the scores in condition one to be lower than the scores in condition two.

Describe in words what the null and alternative hypotheses state for a two-tailed independent samples t test.

Quiz 10: Two-Sample T-Test: Independent Samples Design

If α = .01 and p > .01 for a two-tailed independent samples t test, then we can conclude that

The mean stubbornness scores for the 8 individuals in sample A was 36. The mean for sample B, consisting of 12 individuals, was 42. A two-tailed independent samples t test was conducted and tobt = +2.33. Given an α = .05, we can conclude that

A two-tailed independent samples t test was conducted with an α = .01. The mean for group A, consisting of 8 individuals, was 63. The mean for group B, consisting of 9 individuals, was 61. If the obtained t-value was -2.63, we could conclude that

In a two-tailed independent samples t test, the null hypothesis specifies the difference between means values to be ________.

If SS for group one is 32 and SS for group two is 51 and both groups are made up of 7 individuals, what is ?

The difference between M₁ and M₂ is 12. The pooled variance is 5. Which of the following can be used to determine Cohen's d for an independent samples t test?

The difference between means is 4. The pooled variance is 9. What is the value of Cohen's d for an independent samples t test?

The following results were reported for an independent samples t test: t(21) = -2.32, p > .01. The results suggest that

The following results were reported for an independent samples t test: t(18) = +2.15, p < .05. The results suggest that

If our obtained t-value for an independent samples t test is -2.21 and we are using a nondirectional alternative hypothesis, which of the following tcrit value(s) will lead to the rejection of H₀?

Given a tcrit of -2.01 for an independent samples t test, which of the following obtained t-value will lead to the rejection of H₀?

For an independent samples t test, the ________ the difference between the sample means, the ________ the likelihood of rejecting H₀.

Which of the following is not one of the assumptions of the independent samples t test?

The homogeneity of variance assumption for the independent samples t test requires that

Explain the difference between a one-sample t test and an independent samples t test.

Using symbolic notation, write the null and alternative hypotheses for a two-tailed independent samples t test.

Using symbolic notation, write the null and alternative hypotheses for a one-tailed independent samples t test for which the researcher expects the scores in condition one to be higher than the scores in condition two.

Using symbolic notation, write the null and alternative hypotheses for a one-tailed independent samples t test for which the researcher expects the scores in condition one to be lower than the scores in condition two.

Describe in words what the null and alternative hypotheses state for a two-tailed independent samples t test.

The mean stubbornness scores for the 8 individuals in sample A was 36. The mean for sample B, consisting of 12 individuals, was 42. A two-tailed independent samples t test was conducted and t_obt = +2.33. Given an α = .05, we can conclude that

If our obtained t-value for an independent samples t test is -2.21 and we are using a nondirectional alternative hypothesis, which of the following t_crit value(s) will lead to the rejection of H₀?

Given a t_crit of -2.01 for an independent samples t test, which of the following obtained t-value will lead to the rejection of H₀?

For an independent samples t test, the the difference between the sample means, the the likelihood of rejecting H₀.