Which of the following statements about the two sample sizes is NOT true? Assume thepopulation standard deviations are equal
A. Sample A = 11; sample B = 13
B. Sample A = 12; sample B = 14
C. Sample A = 13; sample B = 13
D. Sample A = 10; sample B = 16
To determine which statement is not true, we need to compare the sample sizes provided in each statement and identify any discrepancies.
Statement A: Sample A = 11; sample B = 13
This statement does not provide any information about the sample sizes, so we cannot determine if it is true or not. Move on to the next statement.
Statement B: Sample A = 12; sample B = 14
Again, this statement does not provide any information about the sample sizes. Move on to the next statement.
Statement C: Sample A = 13; sample B = 13
Both samples have the same size, which is 13. This statement is true because it assumes the population standard deviations are equal.
Statement D: Sample A = 10; sample B = 16
Here, sample A has a size of 10 while sample B has a size of 16. Since the sample sizes are not equal, this statement is not true.
Therefore, the statement that is NOT true is D. Sample A = 10; sample B = 16.
The correct answer is D. Sample A = 10; sample B = 16.
This statement is not true because the two sample sizes are different. In order for the population standard deviations to be equal, the sample sizes need to be the same. Therefore, option D is the answer as it does not follow this condition.