Question 1

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 estimated standard error for the sample mean difference is calculated using the formula: sqrt((pooled variance/n1) + (pooled variance/n2)). Here, n1 = n2 = 6, so it becomes sqrt((20/6) + (20/6)).

Question 2

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

When the independent-measures t statistic is used, the degrees of freedom are calculated using the formula:
df = n1 + n2 - 2
Where n1 and n2 are the sample sizes.

Since the degrees of freedom (df) is reported as 30, we can set up an equation:
30 = n1 + n2 - 2
If the two samples are the same size, then we can simplify the equation:
30 = 2n - 2 
where n is the sample size

Solving for n, we get:
n = (30 + 2)/2 
n = 16

Therefore, the answer is B, with each sample having n = 16.

Question 3

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 t statistic is calculated using the formula: t = (M1 - M2) / sqrt(s^2/n1 + s^2/n2). Here, M1 - M2 = 4, s^2 = 12, n1 = n2 = 6. So, t = 4 / sqrt(12/6 + 12/6) = 4 / sqrt(4) = 4 / 2 = 2.

Question 4

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 5

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 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 6

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

Accepted Answer

If t = 0 in an independent-measures hypothesis test, it indicates that the difference between the two sample means is zero, meaning the two sample means must be equal.

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, 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 8

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.

Question 9

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 10

Which of the following accurately describes an independent-measures study?

Accepted Answer

An independent-measures study, also known as a between-subjects design, involves using different groups of participants for each treatment condition.

Question 11

An independent-measures research study uses two samples, each with n = 12 participants.If the data produce a t statistic of t = 2.08, then which of the following is the correct decision for a two-tailed hypothesis test?

Accepted Answer

With n = 12 in each group, the degrees of freedom is 22. For a two-tailed test with α = .05, the critical t value is approximately 2.074. Since 2.08 > 2.074, we reject the null hypothesis at α = .05. For α = .01, the critical t value is approximately 2.819, and since 2.08 < 2.819, we fail to reject the null hypothesis at α = .01.

Question 12

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

If the t statistic has df = 18 and the two samples are the same size, then each sample has n = (18 + 2)/2 = 10 participants.

Question 13

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

Accepted Answer

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

Question 14

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 15

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

The pooled variance is a weighted average of the two variances, with weights proportional to the sample sizes. Since the second sample has more scores (n=15) than the first sample (n=10), the pooled variance will be closer to the variance of the second sample, which is 30.

Question 16

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 17

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 is the average of the two variances when the sample sizes are equal. Therefore, (10 + 6) / 2 = 8.

Question 18

An independent-measures research study uses two samples, each with n = 12 participants.If the data produce a t statistic of t = 2.50, then which of the following is the correct decision for a two-tailed hypothesis test?

Accepted Answer

With 22 degrees of freedom (n1 + n2 - 2 = 24 - 2 = 22), the critical t-value for α = .05 is approximately 2.074 and for α = .01 is approximately 2.819. Since 2.50 is greater than 2.074 but less than 2.819, we reject the null hypothesis at α = .05 but fail to reject at α = .01.

Question 19

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

Accepted Answer

The answer of What is the pooled variance for the...

Question 20

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 answer of One sample has n = 5 scores...

Quiz 10: The T Test for Two Independent Samples

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?

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 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 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?

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

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

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 _____.

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

Which of the following accurately describes an independent-measures study?

An independent-measures research study uses two samples, each with n = 12 participants.If the data produce a t statistic of t = 2.08, then which of the following is the correct decision for a two-tailed hypothesis test?

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?

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

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 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?

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?

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?

An independent-measures research study uses two samples, each with n = 12 participants.If the data produce a t statistic of t = 2.50, then which of the following is the correct decision for a two-tailed hypothesis test?

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

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?

Quiz 10: The T Test for Two Independent Samples

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?

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 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 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?

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

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

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 _____.

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

Which of the following accurately describes an independent-measures study?

An independent-measures research study uses two samples, each with n = 12 participants.If the data produce a t statistic of t = 2.08, then which of the following is the correct decision for a two-tailed hypothesis test?

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?

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

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 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?

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?

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?

An independent-measures research study uses two samples, each with n = 12 participants.If the data produce a t statistic of t = 2.50, then which of the following is the correct decision for a two-tailed hypothesis test?

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

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?

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 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 ______.

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 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 $\mathrm{SS}=168 \\$ Sample $2: \mathrm{n}=6$ and SS $=120$