Question 1

An independent-measures study comparing two treatment conditions produces a t statistic with df = 18.If the two samples are the same size,how many participants were in each of the samples?
A)9
B)10
C)19
D)20

Accepted Answer

When the degrees of freedom (df) are 18 and the two samples are equal in size, each sample contains 10 participants. This can be determined from a t-distribution table or by using a calculator or software program that calculates t-tests.

Question 2

One sample has n = 10 scores and a variance of s² = 20,and a second sample has n = 15 scores and a variance of s² = 30.What can you conclude about the pooled variance for these two samples? A)It will be closer to 20 than to 30. B)It will be closer to 30 than to 20. C)It will be exactly halfway between 20 and 30. D)Cannot be determined without more information.

Accepted Answer

The pooled variance is a weighted average of the variances of the two samples, with greater weight given to the sample with the larger variance. Therefore, the pooled variance will be closer to the variance of the second (larger variance) sample, which is 30.

Question 3

One sample has n = 5 scores and the second has n = 10 scores.If the pooled variance for the two samples is 30,what is the value of the estimated standard error for the sample mean difference?
A)2
B)The square root of 2
C)9
D)3

Accepted Answer

D

Question 4

An independent-measures study with n = 6 in each sample produces a sample mean difference of 4 points and a pooled variance of 12.What is the value for the t statistic?
A)1
B)2
C)4/$\surd$2
D)4/$\surd$8

Accepted Answer

The answer of An independent-measures study with n = 6...

Question 5

An independent-measures study has one sample with n = 6 and a second sample with n = 8 to compare two experimental treatments.What is the df value for the t statistic for this study?
A)7
B)12
C)13
D)14

Accepted Answer

The df value for an independent-measures t-test is calculated by subtracting 2 from the total number of participants (n1 + n2 - 2). Therefore, in this study, df = 6 + 8 - 2 = 12.

Question 6

Which of the following research situations would be most likely to use an independent-measures design? A)Examine the development of vocabulary as a group of children mature from age 2 to age 3 B)Examine the long-term effectiveness of a stop-smoking treatment by interviewing subjects 2 months and 6 months after the treatment ends C)Compare the mathematics skills for 9^th-grade boys versus 9^th-grade girls D)Compare the blood-pressure readings before medication and after medication for a group a patients with high blood pressure

Accepted Answer

An independent-measures design involves comparing two separate groups, such as boys versus girls in this case, rather than measuring the same group at different time points (A), comparing the same group before and after treatment (D), or interviewing the same subjects at different time points (B).

Question 7

The data from an independent-measures research study produce a sample mean difference of 6 points and an estimated standard error of 2 points.If there are n = 8 scores in each sample,what is the value for the t statistic?
A)6/2
B)6/4
C)6/0.25
D)6/0.50

Accepted Answer

The t statistic is calculated by dividing the sample mean difference by the estimated standard error. In this case, it is 6 points divided by 2 points, which equals 3. Therefore, the correct choice is A) 6/2.

Question 8

If an independent-measures design is being used to compare two treatment conditions,then how many different groups of participants would be needed and how many scores would there be for each participant?
A)1 group,1 score each
B)2 groups,1 score each
C)1 group,2 scores each
D)2 groups,2 scores each

Accepted Answer

In an independent-measures design, each participant is only in one group and only provides one score, thus requiring two different groups of participants to compare two treatment conditions.

Question 9

Which of the following is the correct null hypothesis for an independent-measures t test? A)μ₁ - μ₂ = 0 B)M₁ - M₂ = 0 C)μ₁ - μ₂ 0 D)M₁ - M₂ 0

Accepted Answer

The null hypothesis for an independent-measures t test states that there is no difference between the population means, represented as μ₁ - μ₂ = 0.

Question 10

One sample has a variance of s² = 10 and a second sample has a variance of s² = 6.Which of the following most accurately describes the pooled variance for the two samples? A)Closer to 6 than to 10 B)Closer to 10 than to 6 C)Somewhere between 6 and 10 D)Around 16

Accepted Answer

The pooled variance is calculated as the weighted average of the variances of the individual samples, where the weights are proportional to the degrees of freedom of each sample. Since both samples have equal size and are assumed to have equal variance, the degrees of freedom for each sample are n-1. The pooled variance is therefore: 
(s1^2)*(n1-1) + (s2^2)*(n2-1) / (n1+n2-2) 
= (10*9 + 6*9) / 16 
= 54 / 16 
≈ 3.375 
This value is between 6 and 10, so the answer is C.

Question 11

An independent-measures research study uses a total of 40 participants to compare two treatment conditions.What is the df value for the t statistic for this study?
A)18
B)19
C)38
D)39

Accepted Answer

The df value for an independent-measures t-test is calculated by adding the sample sizes of both groups and subtracting 2. In this study, since there are 2 treatment conditions, each with 20 participants, the total sample size is 40. Therefore, the df value would be 40-2=38. So, the correct answer is (C).

Question 12

A researcher reports an independent-measures t statistic with df = 30.If the two samples are the same size (n₁ = n₂),then how many individuals are in each sample? A)n = 15 B)n = 16 C)n = 30 D)n = 31

Accepted Answer

When the two samples are the same size, the degrees of freedom (df) for the independent-measures t test is calculated as follows: df = 2n - 2, where n is the sample size.

Substitute df = 30 into the formula: 
30 = 2n - 2 
32 = 2n 
n = 16

Therefore, each sample has n = 16 individuals. 
The answer is choice B.

Question 13

A researcher reports an independent-measures t statistic with df = 16.How many participants were in the entire study?
A)17
B)18
C)33
D)34

Accepted Answer

For an independent-measures t-test, the degrees of freedom (df) are calculated as the sum of the sample sizes of the two groups minus 2 (df = n1 + n2 - 2). Given df = 16, solving for the total number of participants (n1 + n2) gives us 18 (16 + 2 = 18).

Question 14

An independent-measures study uses n = 15 participants in each group to compare two treatment conditions.What is the df value for the t statistic for this study?
A)14
B)15
C)28
D)29

Accepted Answer

The df value for a two-sample t-test with equal sample sizes is (n1 + n2) - 2. Therefore, in this study, the df value would be (15 + 15) - 2 = 28. So, the correct choice is C.

Question 15

Two samples,each with n = 5 scores,have a pooled variance of 40.What is the estimated standard error for the sample mean difference?
A)4
B)8
C)10
D)20

Accepted Answer

The estimated standard error for the sample mean difference is calculated using the formula: $\sqrt{\frac{2(S_p^2)}{n}}$, where $S_p^2$ is the pooled variance and $n$ is the sample size for each group. Substituting the given values, we get $\sqrt{\frac{2(40)}{5}} = \sqrt{16} = 4$.

Question 16

Two samples,each with n = 16 scores,produce an estimated standard error of 4 points and a t statistic of t = 2.00.What is the sample mean difference?
A)2
B)4
C)8
D)16

Accepted Answer

Using the formula for the t statistic:
t = (M1 - M2) / (SE)
where M1 and M2 are the sample means and SE is the estimated standard error.
Therefore, we can solve for the mean difference:
(M1 - M2) = t * SE
(M1 - M2) = 2 * 4
(M1 - M2) = 8
So the sample mean difference is 8, which corresponds to choice C.

Question 17

One sample of n = 8 scores has a variance of s² = 6 and a second sample of n = 8 scores has s² = 10.If the pooled variance is computed for these two samples,then the value obtained will be ______. A)closer to 6 than to 10 B)closer to 10 than to 6 C)exactly halfway between 6 and 10 D)cannot be determined without more information

Accepted Answer

The answer of One sample of n = 8 scores...

Question 18

Two samples each have n = 4 scores.If the first sample has a variance of 10 and the second sample has a variance of 6,what is the estimated standard error for the sample mean difference?
A)1
B)2
C)4
D)Cannot determine without more information

Accepted Answer

The estimated standard error for the sample mean difference can be calculated using the formula, 
SE = sqrt((s1^2/n1) + (s2^2/n2)), where s1 and s2 are the variances of the two samples and n1 and n2 are the sample sizes. Plugging in the values, we get SE = sqrt((10/4) + (6/4)) = sqrt(4) = 2. Therefore, the estimated standard error is 2.

Question 19

The data from an independent-measures research study produce a sample mean difference of 4 points and a pooled variance of 18.If there are n = 4 scores in each sample,what is the estimated standard error for the sample mean difference?
A)3
B)9
C)12
D)The square root of 12

Accepted Answer

The answer of The data from an independent-measures research study...

Question 20

What is the pooled variance for the following two samples?
A)7 Sample 1: n = 8 and SS = 168
B)$\surd$7 Sample 2: n = 6 and SS = 120
C)20.57
D)24

Accepted Answer

The pooled variance is calculated using the formula: (SS1 + SS2) / (n1 + n2 - 2). For these samples, it is (168 + 120) / (8 + 6 - 2) = 24.

Quiz 10: The T Test for Two Independent Samples

An independent-measures study comparing two treatment conditions produces a t statistic with df = 18.If the two samples are the same size,how many participants were in each of the samples?

One sample has n = 10 scores and a variance of s² = 20,and a second sample has n = 15 scores and a variance of s² = 30.What can you conclude about the pooled variance for these two samples?

One sample has n = 5 scores and the second has n = 10 scores.If the pooled variance for the two samples is 30,what is the value of the estimated standard error for the sample mean difference?

An independent-measures study with n = 6 in each sample produces a sample mean difference of 4 points and a pooled variance of 12.What is the value for the t statistic?

An independent-measures study has one sample with n = 6 and a second sample with n = 8 to compare two experimental treatments.What is the df value for the t statistic for this study?

Which of the following research situations would be most likely to use an independent-measures design?

The data from an independent-measures research study produce a sample mean difference of 6 points and an estimated standard error of 2 points.If there are n = 8 scores in each sample,what is the value for the t statistic?

If an independent-measures design is being used to compare two treatment conditions,then how many different groups of participants would be needed and how many scores would there be for each participant?

Which of the following is the correct null hypothesis for an independent-measures t test?

One sample has a variance of s² = 10 and a second sample has a variance of s² = 6.Which of the following most accurately describes the pooled variance for the two samples?

An independent-measures research study uses a total of 40 participants to compare two treatment conditions.What is the df value for the t statistic for this study?

A researcher reports an independent-measures t statistic with df = 30.If the two samples are the same size (n₁ = n₂) ,then how many individuals are in each sample?

A researcher reports an independent-measures t statistic with df = 16.How many participants were in the entire study?

An independent-measures study uses n = 15 participants in each group to compare two treatment conditions.What is the df value for the t statistic for this study?

Two samples,each with n = 5 scores,have a pooled variance of 40.What is the estimated standard error for the sample mean difference?

Two samples,each with n = 16 scores,produce an estimated standard error of 4 points and a t statistic of t = 2.00.What is the sample mean difference?

One sample of n = 8 scores has a variance of s² = 6 and a second sample of n = 8 scores has s² = 10.If the pooled variance is computed for these two samples,then the value obtained will be ______.

Two samples each have n = 4 scores.If the first sample has a variance of 10 and the second sample has a variance of 6,what is the estimated standard error for the sample mean difference?

The data from an independent-measures research study produce a sample mean difference of 4 points and a pooled variance of 18.If there are n = 4 scores in each sample,what is the estimated standard error for the sample mean difference?

What is the pooled variance for the following two samples?