When to know whether the given data is paired data or independent data? For example in these two questions, how do we identify which between these two is paired data? In order to increase the efficiency with which employees in a certain organisation can carry out a task, 5 employees are sent on a training course. The time in seconds to carry out the task both before and after the training course is given below for the 5 employees: A B C D E Before 42 51 37 43 45 After 38 37 32 40 48 A car manufacturer runs tests to investigate the fuel consumption of cars using a newly developed fuel additive. Sixteen cars of the same make and age are used, eight with the new additive and eight as controls. The results, in miles per gallon over a test track under regulated conditions, are as follows: Control 27.0 32.2 30.4 28.0 26.5 25.5 29.6 27.2 Additive 31.4 29.9 33.2 34.4 32.0 28.7 26.1 30.3 If C is the mean number of miles per gallon achieved by cars in the control group, and A is the mean number of miles per gallon achieved by cars in the group with fuel additive, test: H0 :m A - mC = 0 vs H1 :mA - mC > 0
Paired data is used for dependent samples. It is a problem of single sample actually . In this first example- The employees are same for both samples but their efficiency is measured before and after training( for same employees). But in second example- cars are not same for both samples so they are independent. Paired data can arise in form 'Before and After' comparisons.
You can mention the question no. for your queries if it's a question of course notes. Writing down whole qus., such effort is not needed.
Thanks for the advice! I have a soft copy of the material, so I am able to quickly copy paste the questions, making it a bit easier for the reader.
