Use the following information for questions:
It is known that for right-handed people, the dominant (right) hand tends to be stronger. For left-handed people who live in a world designed for right-handed people, the same may not be true. To test this, muscle strength was measured on the right and left hands of a random sample of 15 left-handed men and the difference (left - right) was found. The alternative hypothesis is one-sided (left hand stronger). The resultingt-statistic was 1.80.
-Which of the following is true about the conditions necessary to carry out the t-test in this situation?
A) Because the sample size is small (15), the population of differences must be assumed to be approximately normal, but no assumption about the variances is required.
B) Because the sample size is not small (15 + 15 = 30), the population of differences need not be assumed to be approximately normal, and no assumption about the variances is required.
C) Because the sample size is small (15), the population of differences must be assumed to be approximately normal, and the variances of the right and left hand strengths must be assumed to be equal.
D) Because the sample size is not small (15 + 15 = 30), the population of differences need not be assumed to be approximately normal, but the variances of the right and left hand strengths must be assumed to be equal.

Question

Use the following information for questions:
 It is known that for right-handed people, the dominant (right) hand tends to be stronger. For left-handed people who live in a world designed for right-handed people, the same may not be true. To test this, muscle strength was measured on the right and left hands of a random sample of 15 left-handed men and the difference (left - right) was found. The alternative hypothesis is one-sided (left hand stronger). The resultingt-statistic was 1.80.
-Which of the following is true about the conditions necessary to carry out the t-test in this situation?
A) Because the sample size is small (15), the population of differences must be assumed to be approximately normal, but no assumption about the variances is required.
B) Because the sample size is not small (15 + 15 = 30), the population of differences need not be assumed to be approximately normal, and no assumption about the variances is required.
C) Because the sample size is small (15), the population of differences must be assumed to be approximately normal, and the variances of the right and left hand strengths must be assumed to be equal.
D) Because the sample size is not small (15 + 15 = 30), the population of differences need not be assumed to be approximately normal, but the variances of the right and left hand strengths must be assumed to be equal.

Quizplus · Accepted Answer

For a t-test, especially with a small sample size (n < 30), it is necessary to assume that the population from which the sample is drawn is approximately normally distributed. This test does not require assumptions about the equality of variances when dealing with the differences in paired samples (such as left hand strength minus right hand strength).

Use the Following Information for Questions