Question 1

The independent-measures t statistic uses the data from two separate samples to draw inferences about the mean difference between two populations or between two different treatment conditions.​

Accepted Answer

The independent-measures t statistic is a statistical test that uses separate samples to draw inferences about the mean difference between two populations or treatment conditions.

Question 2

If the two samples are the same size,the independent measures t statistic will have an even number for degrees of freedom.​

Accepted Answer

If the two samples are the same size, the degrees of freedom for the independent measures t statistic will be (n1 + n2 - 2), which is an even number. This is because in this case, the degrees of freedom are determined by subtracting 2 from the sum of the sample sizes. If the sample sizes are the same, their sum will be an even number, and subtracting 2 from that will also result in an even number.

Question 3

​If an independent-measures t statistic has df = 20,then there were a total of 18 individuals participating in the research study.

Accepted Answer

The degrees of freedom (df) for an independent-measures t statistic with 18 individuals would be df = 16, not df = 20. Therefore, the statement is false.

Question 4

​The results from an independent-measures t hypothesis test are reported as "t(14)= 2.13,p > .05,two tailed."For this test,the null hypothesis was rejected.

Accepted Answer

The given results show that the calculated t-value is 2.13, degrees of freedom (df) are 14, and the p-value is greater than .05 for a two-tailed test. This means that the test was not statistically significant at the .05 level. Since the null hypothesis is typically rejected only if the p-value is less than .05 (or the alpha level chosen), in this case, we fail to reject the null hypothesis. Therefore, the correct answer is option B, False.

Question 5

​One method for correcting the bias in the standard error is to "pool" the two sample variances using a procedure that allows the bigger sample to carry more weight in determining the final value of the variance.

Accepted Answer

Pooling the sample variances is a common method for correcting the bias in the standard error, where the variance estimate is based on the combined data from two or more samples. In this method, the larger sample size is given more weight in determining the final value of the variance estimate. Therefore, option A is correct.

Question 6

If the df value for an independent-measures t statistic is an odd number,then it is impossible for the two samples to be the same size.

Accepted Answer

The degrees of freedom (df) for an independent-measures t test is calculated as follows:

df = (n1 - 1) + (n2 - 1)

where n1 and n2 are the sample sizes for Group 1 and Group 2, respectively.

If the df value is an odd number, this means that (n1 - 1) and (n2 - 1) must both be odd or both be even. If they were both even, their sum would be even, not odd. Therefore, the two sample sizes cannot be the same.

Question 7

​Two separate samples,each with n = 10 scores,will produce an independent-measures t statistic with df = 19.

Accepted Answer

For independent-measures t-tests, the degrees of freedom formula is typically (n1 + n2 - 2). Therefore, for two separate samples with n=10, the degrees of freedom would be (10+10-2) = 18, not 19.

Question 8

For an independent-measures t statistic,the estimated standard error measures how much difference is reasonable to expect between the two sample means if the null hypothesis is true.​

Accepted Answer

The estimated standard error in independent-measures t statistic measures the standard deviation of the sampling distribution of the sample mean difference. It determines how much difference is reasonable to expect between the two sample means if the null hypothesis is true. Therefore, the statement is true.

Question 9

?Two samples,each with n = 4 scores,have a pooled variance of 32.The estimated standard error for the sample mean difference is $\sqrt { 8 }$ .

Accepted Answer

The answer of ?Two samples,each with n = 4 scores,have...

Question 10

​For a hypothesis test with the independent-measures t statistic,the null hypothesis states that the two population means are the same and the homogeneity assumption states that the two population variances are the same.

Accepted Answer

This is the standard assumption for the independent-measures t-test. The null hypothesis is that the means of two populations are equal, and the homogeneity assumption is that the variances of the two populations are equal.

Question 11

When pooling variances,the resulting value will be closer to the variance for the sample with the smaller number of scores.​

Accepted Answer

When pooling variances, the resulting value is a weighted average of the individual sample variances, typically giving more weight to the variance of the sample with the larger number of observations, not the smaller.

Question 12

The null hypothesis for the independent-measures t test states that there is no difference between the two sample means.

Accepted Answer

The null hypothesis for the independent-measures t test states that there is no difference between the two population means, not the sample means.

Question 13

For an independent-measures t statistic,you typically must compute the pooled variance before calculating the estimated standard error.​

Accepted Answer

This statement is true. The pooled variance is necessary to calculate the estimated standard error in an independent-measures t statistic.

Question 14

If two sample variances are not equal,the pooled variance will be closer to the larger of the two variances.​

Accepted Answer

The pooled variance in this case will be more heavily influenced by the larger sample size, but it is not necessarily closer to the larger variance. The formula for pooled variance takes into account both sample sizes and variances, so it is not accurate to simply say that it will be closer to the larger variance. In fact, if one sample size is much larger than the other, the pooled variance may be closer to the smaller variance.

Question 15

If both samples have the same number of scores (n),then the independent-measures t statistic will have df = 2n - 2.​

Accepted Answer

This is true. When both samples have the same number of scores, the total number of degrees of freedom is equal to the sum of the degrees of freedom for each sample, which is 2n-2. This is because each sample has n-1 degrees of freedom for estimating the population variance, and there are two samples.

Question 16

The estimated standard error for the independent-measures t statistic provides a measure of how much difference should exist,on average,between two sample means for samples selected from the same population.​

Accepted Answer

The estimated standard error for the independent-measures t statistic provides a measure of the variability in the difference between two sample means that can be attributed to chance or sampling error, assuming the two samples are selected from the same population. Therefore, option A is true.

Question 17

​If one sample has n = 5 scores with SS = 40 and a second sample has n = 5 scores with SS = 20,then the pooled variance will be 60/10 = 6.

Accepted Answer

The pooled variance is calculated by dividing the sum of the squared deviations for both samples by the degrees of freedom, which is n1 + n2 - 2. The correct calculation for pooled variance in this case is (40+20)/(5+5-2) = 6. However, the question incorrectly states that the pooled variance is 60/10.

Question 18

If two samples each have s² = 10,then the pooled variance will be equal to 20,regardless of sample size.

Accepted Answer

The pooled variance is a weighted average of the variances of two samples, taking into account their sample sizes. It does not simply add the variances together, so it would not necessarily equal 20.

Question 19

​If the two samples are the same size,then the pooled variance will equal the average of the two sample variances.

Accepted Answer

This statement is true. When the two samples are the same size, the pooled variance is calculated as the average of the two sample variances. This is because when the sample sizes are equal, we assume that the two groups have the same population variance, and so we estimate the population variance by pooling the variances of the two samples together.

Question 20

​One sample has n = 7 scores with SS = 40,and a second sample has n = 5 scores with SS = 80.The pooled variance for these two samples is 120/10 = 12.

Accepted Answer

The pooled variance is calculated as the sum of the variances of the two samples divided by the total number of samples. In this case, the pooled variance is (40 + 80) / (7 + 5) = 120 / 12 = 10.

Quiz 10: The T Test for Two Independent Samples

The independent-measures t statistic uses the data from two separate samples to draw inferences about the mean difference between two populations or between two different treatment conditions.​

If the two samples are the same size,the independent measures t statistic will have an even number for degrees of freedom.​

​If an independent-measures t statistic has df = 20,then there were a total of 18 individuals participating in the research study.

​The results from an independent-measures t hypothesis test are reported as "t(14)= 2.13,p > .05,two tailed."For this test,the null hypothesis was rejected.

​One method for correcting the bias in the standard error is to "pool" the two sample variances using a procedure that allows the bigger sample to carry more weight in determining the final value of the variance.

If the df value for an independent-measures t statistic is an odd number,then it is impossible for the two samples to be the same size.

​Two separate samples,each with n = 10 scores,will produce an independent-measures t statistic with df = 19.

For an independent-measures t statistic,the estimated standard error measures how much difference is reasonable to expect between the two sample means if the null hypothesis is true.​

?Two samples,each with n = 4 scores,have a pooled variance of 32.The estimated standard error for the sample mean difference is 8\sqrt { 8 }8​ .

​For a hypothesis test with the independent-measures t statistic,the null hypothesis states that the two population means are the same and the homogeneity assumption states that the two population variances are the same.

When pooling variances,the resulting value will be closer to the variance for the sample with the smaller number of scores.​

The null hypothesis for the independent-measures t test states that there is no difference between the two sample means.

For an independent-measures t statistic,you typically must compute the pooled variance before calculating the estimated standard error.​

If two sample variances are not equal,the pooled variance will be closer to the larger of the two variances.​

If both samples have the same number of scores (n),then the independent-measures t statistic will have df = 2n - 2.​

The estimated standard error for the independent-measures t statistic provides a measure of how much difference should exist,on average,between two sample means for samples selected from the same population.​

​If one sample has n = 5 scores with SS = 40 and a second sample has n = 5 scores with SS = 20,then the pooled variance will be 60/10 = 6.

​If two samples each have s2 = 10,then the pooled variance will be equal to 20,regardless of sample size.

​If the two samples are the same size,then the pooled variance will equal the average of the two sample variances.

​One sample has n = 7 scores with SS = 40,and a second sample has n = 5 scores with SS = 80.The pooled variance for these two samples is 120/10 = 12.

The independent-measures t statistic uses the data from two separate samples to draw inferences about the mean difference between two populations or between two different treatment conditions.

If the two samples are the same size,the independent measures t statistic will have an even number for degrees of freedom.

If an independent-measures t statistic has df = 20,then there were a total of 18 individuals participating in the research study.

The results from an independent-measures t hypothesis test are reported as "t(14)= 2.13,p > .05,two tailed."For this test,the null hypothesis was rejected.

One method for correcting the bias in the standard error is to "pool" the two sample variances using a procedure that allows the bigger sample to carry more weight in determining the final value of the variance.

Two separate samples,each with n = 10 scores,will produce an independent-measures t statistic with df = 19.

For an independent-measures t statistic,the estimated standard error measures how much difference is reasonable to expect between the two sample means if the null hypothesis is true.

?Two samples,each with n = 4 scores,have a pooled variance of 32.The estimated standard error for the sample mean difference is $\sqrt { 8 }$ .

For a hypothesis test with the independent-measures t statistic,the null hypothesis states that the two population means are the same and the homogeneity assumption states that the two population variances are the same.

When pooling variances,the resulting value will be closer to the variance for the sample with the smaller number of scores.

For an independent-measures t statistic,you typically must compute the pooled variance before calculating the estimated standard error.

If two sample variances are not equal,the pooled variance will be closer to the larger of the two variances.

If both samples have the same number of scores (n),then the independent-measures t statistic will have df = 2n - 2.

The estimated standard error for the independent-measures t statistic provides a measure of how much difference should exist,on average,between two sample means for samples selected from the same population.

If one sample has n = 5 scores with SS = 40 and a second sample has n = 5 scores with SS = 20,then the pooled variance will be 60/10 = 6.

If two samples each have s² = 10,then the pooled variance will be equal to 20,regardless of sample size.

If the two samples are the same size,then the pooled variance will equal the average of the two sample variances.

One sample has n = 7 scores with SS = 40,and a second sample has n = 5 scores with SS = 80.The pooled variance for these two samples is 120/10 = 12.