Question

When the two population means are equal, the estimated standard error for the independent-measures t test provides a measure of how much difference to expect between two sample means. For each of the following situations, assume that

and calculate how much difference should be expected between the two sample means.

a. One sample has n = 6 scores with SS = 70 and the second sample has n = 10 scores with SS = 140.

b. One sample has n = 6 scores with SS = 310 and the second sample has n = 10 scores with SS = 530.

c. In Part b, the samples have larger variability than in Part a, but the sample sizes are unchanged. How does larger variability affect the magnitude of the standard error for the sample mean difference?

Group of answer choices

larger variability produces a larger standard error.

For question b, the estimated standard error = 8.

For question a, the estimated standard error = 6.

For question b, the estimated standard error = 10.

For question a, the estimated standard error = 15.

Larger variability produces a smaller standard error.

Smaller variability produces a larger standard error.

For question a, the estimated standard error = 2.

For question b, the estimated standard error = 4.

Answer 1

The estimated standard error for the independent-measures t test provides a measure of how much difference to expect between two sample means when the population means are equal. For each situation, we calculate the standard error using the given formulas for the samples' sizes and sum of squares. In situation c, larger variability leads to a larger standard error.

Step-by-step explanation:

The estimated standard error for the independent-measures t test provides a measure of how much difference to expect between two sample means when the population means are equal.

For each situation, we need to calculate the standard error using the formula:

Standard Error = sqrt((SS1/n1 + SS2/n2) / (n1 + n2 - 2))

a. One sample has n = 6 scores with SS = 70 and the second sample has n = 10 scores with SS = 140:
Standard Error = sqrt((70/6 + 140/10) / (6 + 10 - 2)) = sqrt((11.67 + 14) / 14) = sqrt(1.405) = 1.18

b. One sample has n = 6 scores with SS = 310 and the second sample has n = 10 scores with SS = 530:
Standard Error = sqrt((310/6 + 530/10) / (6 + 10 - 2)) = sqrt((51.67 + 53) / 14) = sqrt(7.62) = 2.76

c. In Part b, the samples have larger variability than in Part a, but the sample sizes are unchanged. Larger variability produces a larger standard error.