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

Since the t-statistic has df = 18, the total sample size must be n1 + n2 = 18 + 2 = 20. If the two samples are the same size, each sample would have n = 10 participants. Therefore, choice B is the correct answer.

Question 2

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 the weighted average of the sample variances, where the weights are proportional to the degrees of freedom of each sample. Since we don't know the degrees of freedom for each sample, we can assume they are equal (which is usually conservative).

Using the formula for pooled variance, we get:

s^2_pooled = [(n1-1)*s1^2 + (n2-1)*s2^2] / (n1+n2-2)
             = [(1*10) + (1*6)] / (1+1-2)
             = 8

Therefore, the pooled variance is somewhere between 6 and 10.

Question 3

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 4

One sample of n = 8 scores has a variance of s² = 6 and a second sample of n = 8 scores has a variance of 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 pooled variance is computed as the weighted average of the two variances, taking into account the number of scores in each sample. Since both samples have the same number of scores (n = 8) and the variances are 6 and 10, the pooled variance will be exactly halfway between 6 and 10, which is 8.

Question 5

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 correct null hypothesis for an independent-measures t test is that there is no difference between the means of the two groups being compared. This is represented by the equation μ1 - μ2 = 0, where μ1 and μ2 are the population means of the two groups. Therefore, choice A is the correct answer. Choice B is incorrect because M is used to represent the sample mean, whereas the t test is concerned with population means. Choices C and D are incorrect because they represent alternative hypotheses, which state that there is a difference between the means of the two groups being compared.

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 9th-grade boys versus 9th-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. The scenario that involves comparing 9th-grade boys versus 9th-grade girls represents two separate groups and thus would most likely use an independent-measures design. The other scenarios either involve studying the same group over time (A and B) or comparing the same group before and after receiving treatment (D), which would not require an independent-measures design.

Question 7

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 8

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 estimated standard error for the sample mean difference is the square root of the pooled variance divided by the square root of the sample size. In this case, the pooled variance is 18 and the sample size is 4, so the estimated standard error for the sample mean difference is the square root of 18 divided by the square root of 4, which is 3.

Question 9

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 10

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 degrees of freedom (df) for an independent-measures t-test is calculated using the formula: df = (n1-1) + (n2-1). For this study, n = 15 for each group, so df = (15-1) + (15-1) = 28. Therefore, the correct answer is C) 28.

Question 11

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 12

What is the pooled variance for the following two samples?
A)7 	Sample 1: n = 8 and SS = 168
B)√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 Sample 1, SS1 = 168 and n1 = 8; for Sample 2, SS2 = 120 and n2 = 6. Plugging these into the formula gives (168 + 120) / (8 + 6 - 2) = 288 / 12 = 24.

Question 13

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)15
B)16
C)30
D)31

Accepted Answer

The answer of A researcher reports an independent-measures t statistic...

Question 14

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 the t statistic is calculated as the smaller of the two sample sizes minus 1. In this case, the smaller sample size is 6, so the df value is 6 - 1 = 5.

Question 15

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 16

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 takes into account the size of each sample (n) and their respective variances. Since the second sample is larger (n = 15) and has a higher variance (s² = 30) compared to the first sample (n = 10, s² = 20), the pooled variance will be weighted more towards the variance of the larger sample, making it closer to 30 than to 20.

Question 17

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

The formula for calculating the mean difference is:

Mean difference = t * estimated standard error
Mean difference = 2.00 * 4
Mean difference = 8

Therefore, the sample mean difference is 8. The correct answer is choice C.

Question 18

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)√2
C)9
D)3

Accepted Answer

The estimated standard error for the sample mean difference is calculated using the formula: SE = √(sp²/n1 + sp²/n2), where sp² is the pooled variance, and n1 and n2 are the sample sizes. Substituting the given values: SE = √(30/5 + 30/10) = √(6 + 3) = √9 = 3.

Question 19

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/√2
D)4/√8

Accepted Answer

The t statistic is calculated using the formula $t = \frac{\text{mean difference}}{\sqrt{\frac{\text{pooled variance}}{n}}}$. Substituting the given values, $t = \frac{4}{\sqrt{\frac{12}{6}}} = \frac{4}{\sqrt{2}} = 2$.

Question 20

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.

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 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?

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

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

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

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

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?

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

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 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?

What is the pooled variance for the following two samples?

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?

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?

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?

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?

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 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?

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?