Question

Please Answer Number 2

2. From a group of 80 individuals, a random sample of size seven is to be drawn. Use the random number table in the text's appendix, using the values beginning at the left end of row 21, to explain how to do this. Show all work. What individuals are included in your sample?

Answer 1

At first we number the individuals serially, in a suitable order, from 1 to 80. Since 80 is two digit number, we consider random numbers in sets of two and assign 01,02,...,80 to the individuals with serial number 1,2,...,80 and the remaining i.e. 00, and the numbers greater than 80 are rejected. Random numbers in sets of two are noted, starting from the left end of row 29 and proceeding row wise (we may proceed column wise also). Suppose the are 33, 18, 02, 20, 36, 11, 98, 87, 46. The following table shows the selection of the sample:

$\begin{matrix} Random ~number & Remark&Sl.~no.~of~the~individual~selected \\ 33 &Accept &33 \\ 18& Accept &18 \\ 02 & Accept &2 \\ 20& Accept &20 \\ 36& Accept &36 \\ 11&Accept &11 \\ 98 &Reject &- \\ 87&Reject &- \\ 46&Accept &46 \end{matrix}$

Note: If you use random sampling without replacement and a random number comes more than one  then select the first and ignore the other repetitions. However this is not required for sampling with replacement.