Question

Psychological tests are often used to determine the hostility levels in people. High scores on the HLT psychological test corresponds to high hostility levels. Suppose that 26 college students, all with equally high HLT test scores, were randomly selected and separated into two groups randomly. Group 1 (10 students) was treated for high hostility levels by using Method A; whereas Group 2 (16 students) was treated for high hostility levels by using Method B. Both groups were treated for a period of 5 months, at which time all 26 students were again given the HLT test. The differences computed are based on Group 1 scores minus Group 2 scores.

The 95% confidence interval for the difference in the mean scores of the two treatment methods is (-11.34, 1.34). Based on this interval, select the best answer below.

O We are 95% confident that there is no statistically significant difference in the mean scores for the two treatment methods.
O We are 95% confident that the mean score for Group 1 using Method A is larger than the mean score for Group 2 using Method B.
O We are 95% confident that the mean score for Group 1 using Method A is smaller than the mean score for Group 2 using Method B.
O None of the above

Answer 1

The correct interpretation of the 95% confidence interval is that there is no statistically significant difference in the mean scores for the two treatment methods because the interval includes zero.

Step-by-step explanation:

The confidence interval for the difference in the mean scores of the two treatment methods is (-11.34, 1.34). This interval includes zero, which indicates that there is not enough evidence to suggest a statistically significant difference between the mean scores of the two methods. Therefore, the correct interpretation is:

We are 95% confident that there is no statistically significant difference in the mean scores for the two treatment methods.

This conclusion was derived based on the fact that the 95% confidence interval ranges from a negative number to a positive one, crossing over zero, suggesting that we cannot confidently say one treatment method is better than the other.