15. Each employee in two separate groups of 15 employees, group I and group II, was given a job-performance rating. The standard deviation of the ratings for group I was 8.5 and the standard deviation for group II was also 8.5. Quantity A: The standard deviation of 30 ratings Quantity B: 17
Answer: D
The relationship cannot be determined from the information given.
The relationship between Quantity A and Quantity B cannot be definitively established based on the provided information about the standard deviations of the two groups. Although both groups have the same standard deviation, combining the two groups' ratings does not allow for a straightforward calculation of the overall standard deviation without additional details regarding the mean ratings of each group.
A) Quantity A is greater.
This option suggests that the standard deviation of the combined ratings would exceed 17. However, without knowing the means of the two groups or how their ratings are distributed, we cannot conclude that the combined standard deviation will necessarily be greater than 17.
B) Quantity B is greater.
This option implies that the standard deviation of the combined ratings is less than 17. As with Option A, without further information about the means or distribution of the ratings, it is impossible to assert that the combined standard deviation would be less than 17.
C) The two quantities are equal.
This option asserts that the standard deviation of the combined ratings equals 17. While both groups have the same standard deviation, the overall standard deviation may vary based on how the ratings in the two groups relate to each other, making it impossible to conclude that they are equal.
D) The relationship cannot be determined from the information given.
This option accurately reflects the uncertainty present in the problem. The equal standard deviations of the two groups do not provide enough information to determine the standard deviation of the combined ratings without additional data about the means or specific rating values.
Conclusion
The correct answer is D because the information provided does not allow for a definitive comparison between the two quantities. Each of the other options makes assumptions about the relationship between the standard deviations that cannot be validated without further data. Therefore, we conclude that the relationship between Quantity A and Quantity B remains indeterminate based on the existing information.