
A sample of 15 weight litters is tested to see how much weight they can bench press. They then follow a special training program for three weeks, alter which they are tested again. The samples are the amounts of weights that were lilted before and after the training program.

Check whether the two samples are independent or paired.
Answer to Problem 1CQ
The two samples are paired.
Explanation of Solution
Calculation:
It is given that, a sample of 15 weight lifters are tested to see the amount of weights lifted by them and a training program is given for 3 weeks for those 15 weight lifters and again tested to see the amount of weights lifted by them. The samples are the amounts of weights lifted by 15 weight lifters before and after the training program.
Independent samples:
Any two randomly selected samples are said to be independent, if the observations in one sample do not depend on the observations in the other sample. In other words it can be said that the observations in one sample should not influence the observations in the other sample.
Paired or dependent samples:
Any two randomly selected samples are said to be paired, if each observation in one sample is paired with the observation in the second sample. In other words it can be said that, if two different drugs are imposed one after another on the same subjects and values of each drug are indicated as a sample, then the two samples are said to be paired o dependent samples.
Here, a single group of individuals is selected. Each and every individual is taken a weight lifting test before and after the training program. This scenario gives two samples of amounts of weights, first sample of weights before the training program and the second sample of weights after the training program.
The investigator compares the weights lifted by weight lifters before and after the training program, to determine the effectiveness of training program.
Here, each observation in one sample can be paired with an observation in second sample. That is, the two samples are dependent.
Thus, the two samples are paired.
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Chapter 9 Solutions
Essential Statistics
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