Question 1

One sample has a variance of s² = 10 and a second sample has a variance of s² = 6.If the two samples have the same number of scores,what is the pooled variance for the two samples?

Accepted Answer

The pooled variance when two samples have the same number of scores is the average of the two variances. Therefore, the pooled variance is (10 + 6) / 2 = 16 / 2 = 8.

Question 2

What is the pooled variance for the following two samples?​Sample 1:n = 8 and SS = 168Sample 2:n = 6 and SS = 120

Accepted Answer

The pooled variance is calculated using the formula: (SS1 + SS2) / (n1 + n2 - 2). Here, SS1 = 168, SS2 = 120, n1 = 8, and n2 = 6. So, pooled variance = (168 + 120) / (8 + 6 - 2) = 288 / 12 = 24.

Question 3

Two samples,each with n = 6 subjects,produce a pooled variance of 20.Based on this information,what is the estimated standard error for the sample mean difference?​

Accepted Answer

The formula to calculate the estimated standard error for the sample mean difference is the square root of [(s1^2/n1) + (s2^2/n2)], where s1 and s2 are the sample standard deviations and n1 and n2 are the sample sizes. Since both samples have the same size and pooled variance, we can use s^2 = 20 as the sample variance for both groups. Therefore, the formula reduces to the square root of [(20/6) + (20/6)], which simplifies to the square root of 20/3. Thus, the estimated standard error for the sample mean difference is the square root of 20/3 or approximately 2.582.

Question 4

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

Accepted Answer

The correct null hypothesis for an independent-measures t test is that the mean score of one group (μ1) is equal to the mean score of the other group (μ2). Therefore, choice A, which represents this hypothesis in mathematical form (μ1 - μ2 = 0), is the best choice. Choices B and D are not valid hypotheses for an independent-measures t test as they refer to specific terms from the analysis of variance (ANOVA), which is a different statistical test. Choice C is not the correct null hypothesis for an independent-measures t test, as it represents a two-tailed alternative hypothesis rather than the null hypothesis.

Question 5

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?

Accepted Answer

Since the sample with n=15 has a larger variance than the sample with n=10, it is likely that the pooled variance will be closer to the larger variance (30) than to the smaller variance (20). Therefore, the correct answer is B.

Question 6

A research design that uses a separate group of participants for each treatment condition(or for each population)is called an independent-measures research designor a____.​

Accepted Answer

A between-subjects design uses separate groups of participants for each treatment condition, making it an independent-measures research design. Repeated-measures designs (A) use the same participants for multiple conditions, while dependent-measures designs (B) measure the same variable multiple times for each participant. Within-subjects designs (D) use the same participants for each treatment condition, making them a type of repeated-measures design.

Question 7

An independent-measures study uses ____.​

Accepted Answer

An independent-measures study involves using a different group of participants for each of the treatment conditions being compared. This is done to ensure that any observed differences between groups are not due to individual differences between participants, but rather due to the effects of the different treatments.

Question 8

​A researcher reports t(22)= 5.30,p < .01 for an independent-measures experiment.How many individuals participated in the entire experiment?

Accepted Answer

The degrees of freedom (df) for an independent-measures t-test is calculated as the sum of the sample sizes of the two groups minus 2. Given df = 22, the total sample size is 22 + 2 = 24 individuals.

Question 9

​In an independent-measures hypothesis test,what must be true if t = 0?

Accepted Answer

When t = 0 in an independent-measures hypothesis test, it means that the difference between the two sample means is zero. This does not necessarily imply anything about the population means, sample variances, or the equality of population means.

Question 10

An independent-measures study has one sample with n = 10 and a second sample with n = 15 to compare two experimental treatments.What is the df value for the t statistic for this study?​

Accepted Answer

The degrees of freedom (df) for an independent-measures t-test is calculated by adding the degrees of freedom from each sample and then combining them. For each sample, df = n - 1. So, for the first sample, df = 10 - 1 = 9, and for the second sample, df = 15 - 1 = 14. Adding these together gives 9 + 14 = 23.

Question 11

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 ____.

Accepted Answer

The pooled variance is the weighted average of the two variances, since both samples have the same size (n = 8), the pooled variance will be exactly halfway between 6 and 10, which is 8.

Question 12

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?​

Accepted Answer

The formula to calculate the t statistic for independent-measures study is: 
t = (M1 - M2) / (Sp * sqrt(2/n))
where M1 - M2 is the mean difference, Sp is the pooled standard deviation, and n is the sample size.

Plugging in the values, we get: 
t = 4 / (sqrt(12) * sqrt(2/6))
t = 4 / (sqrt(2))
t = 2

Therefore, the value for the t statistic is 2, which corresponds to choice letter B.

Question 13

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,then the value for the t statistic is ____.​

Accepted Answer

The t statistic is calculated by dividing the sample mean difference by the estimated standard error. Given a sample mean difference of 6 points and an estimated standard error of 2 points, the t statistic is 6 / 2 = 3.

Question 14

An independent-measures study uses two samples,each with n = 10,to compare two treatment conditions.What is the df value for the t statistic for this study?​

Accepted Answer

The degrees of freedom (df) for an independent-measures t-test is calculated as the sum of the sample sizes of the two groups minus 2. Here, with two groups each having n = 10, df = (10 + 10) - 2 = 20 - 2 = 18.

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??

Accepted Answer

The estimated standard error for the sample mean difference is:$$s_d = \sqrt{\frac{2s^2}{n}} = \sqrt{\frac{2(40)}{5}} = 4$$

Question 16

​Researchers conduct a hypothesis test and use the data from two separate sets of observations drawn from the same group of participants.Their research design is called a repeated-measures research design or a(n)____.

Accepted Answer

A repeated-measures research design is also known as a within-subjects design, where each participant is measured on the same variable more than once. This is in contrast to between-subjects design, where different participants are assigned to different experimental groups, and independent-measures design, where data from two separate groups of participants are compared. Therefore, the best choice is D: within-subjects design.

Question 17

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?​

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 18

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

Accepted Answer

The formula for the estimated standard error for the sample mean difference is:

SE = sqrt[ (s1^2/n1) + (s2^2/n2) ]

where s1^2 and s2^2 are the sample variances for the two groups, and n1 and n2 are the sample sizes.

In this case, we have:

s1^2 = s2^2 = 30 (since we are given the pooled variance)
n1 = 5
n2 = 10

Substituting these values into the formula, we get:

SE = sqrt[ (30/5) + (30/10) ]
SE = sqrt[ 6 + 3 ]
SE = sqrt[ 9 ]
SE = 3

Therefore, the estimated standard error for the sample mean difference is 3. Answer choice C is the only option that matches this calculation.

Question 19

The data from an independent-measures research study produce a sample mean difference of 4 points and a pooled variance of 16.If there are n = 8 scores in each sample,then what is the estimated standard error for the sample mean difference?​

Accepted Answer

The estimated standard error for the sample mean difference is calculated using the formula: SE = sqrt((pooled variance / n) + (pooled variance / n)). Given a pooled variance of 16 and n = 8 for each sample, the calculation is SE = sqrt((16/8) + (16/8)) = sqrt(2 + 2) = sqrt(4) = 2.

Question 20

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?

Accepted Answer

For an independent-measures t-test with equal sample sizes, the degrees of freedom (df) can be calculated as df = 2n - 2, where n is the sample size. 
Here, df = 30, so 30 = 2n - 2. 
Solving for n, we get n = 16. 
Therefore, the best choice is B, with a sample size of n = 16.

Quiz 10: The T Test for Two Independent Samples

One sample has a variance of s² = 10 and a second sample has a variance of s² = 6.If the two samples have the same number of scores,what is the pooled variance for the two samples?

What is the pooled variance for the following two samples?Sample 1:n = 8 and SS = 168Sample 2:n = 6 and SS = 120

Two samples,each with n = 6 subjects,produce a pooled variance of 20.Based on this information,what is the estimated standard error for the sample mean difference?

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

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 research design that uses a separate group of participants for each treatment condition(or for each population) is called an independent-measures research designor a____.

An independent-measures study uses ____.

A researcher reports t(22) = 5.30,p < .01 for an independent-measures experiment.How many individuals participated in the entire experiment?

In an independent-measures hypothesis test,what must be true if t = 0?

An independent-measures study has one sample with n = 10 and a second sample with n = 15 to compare two experimental treatments.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 s² = 10.If the pooled variance is computed for these two samples,then the value obtained will be ____.

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,then the value for the t statistic is ____.

An independent-measures study uses two samples,each with n = 10,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??

Researchers conduct a hypothesis test and use the data from two separate sets of observations drawn from the same group of participants.Their research design is called a repeated-measures research design or a(n) ____.

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 = 5 scores and the second has n = 10 scores.If the pooled variance for the two sample is 30,then what is the value of 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 16.If there are n = 8 scores in each sample,then what is the estimated standard error for the sample mean difference?

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?

Quiz 10: The T Test for Two Independent Samples

One sample has a variance of s2 = 10 and a second sample has a variance of s2 = 6.If the two samples have the same number of scores,what is the pooled variance for the two samples?​

What is the pooled variance for the following two samples?​Sample 1:n = 8 and SS = 168Sample 2:n = 6 and SS = 120

Two samples,each with n = 6 subjects,produce a pooled variance of 20.Based on this information,what is the estimated standard error for the sample mean difference?​

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

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 research design that uses a separate group of participants for each treatment condition(or for each population) is called an independent-measures research designor a____.​

An independent-measures study uses ____.​

​A researcher reports t(22) = 5.30,p < .01 for an independent-measures experiment.How many individuals participated in the entire experiment?

​In an independent-measures hypothesis test,what must be true if t = 0?

An independent-measures study has one sample with n = 10 and a second sample with n = 15 to compare two experimental treatments.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 s2 = 10.If the pooled variance is computed for these two samples,then the value obtained will be ____.

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,then the value for the t statistic is ____.​

An independent-measures study uses two samples,each with n = 10,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??

​Researchers conduct a hypothesis test and use the data from two separate sets of observations drawn from the same group of participants.Their research design is called a repeated-measures research design or a(n) ____.

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 = 5 scores and the second has n = 10 scores.If the pooled variance for the two sample is 30,then what is the value of 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 16.If there are n = 8 scores in each sample,then what is the estimated standard error for the sample mean difference?​

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?​

One sample has a variance of s² = 10 and a second sample has a variance of s² = 6.If the two samples have the same number of scores,what is the pooled variance for the two samples?

What is the pooled variance for the following two samples?Sample 1:n = 8 and SS = 168Sample 2:n = 6 and SS = 120

Two samples,each with n = 6 subjects,produce a pooled variance of 20.Based on this information,what is the estimated standard error for the sample mean difference?

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

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 research design that uses a separate group of participants for each treatment condition(or for each population) is called an independent-measures research designor a____.

An independent-measures study uses ____.

A researcher reports t(22) = 5.30,p < .01 for an independent-measures experiment.How many individuals participated in the entire experiment?

In an independent-measures hypothesis test,what must be true if t = 0?

An independent-measures study has one sample with n = 10 and a second sample with n = 15 to compare two experimental treatments.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 s² = 10.If the pooled variance is computed for these two samples,then the value obtained will be ____.

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,then the value for the t statistic is ____.

An independent-measures study uses two samples,each with n = 10,to compare two treatment conditions.What is the df value for the t statistic for this study?

Researchers conduct a hypothesis test and use the data from two separate sets of observations drawn from the same group of participants.Their research design is called a repeated-measures research design or a(n) ____.

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 = 5 scores and the second has n = 10 scores.If the pooled variance for the two sample is 30,then what is the value of 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 16.If there are n = 8 scores in each sample,then what is the estimated standard error for the sample mean difference?

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?