Question
Draw a random sample of $2$ per cent “students without replacement from $600$ students of a particular college for giving their feedback on faculty members. There are $200$ students in each of the three years ($F.Y., S.Y.$ and $T.Y.$)
Use the following three-digit random numbers :
For $F.Y. : 158, 092, 411, 745, 009, 724, 674, 550, 716, 359, 419, 696, 200, 458.$
For $S.Y.:384, 019, 679, 131, 390, 057, 299, 786, 006, 206, 729, 344, 543, 309.$
For $T.Y.: 227, 483, 741, 766, 027, 070, 648, 956, 198, 912, 200, 058, 696, 500.$

Answer

  • Here, $N =600$
  • $2 \%$ sample without replacement is to be obtained. Therefore. $n =600 \times \frac{2}{100}=12$.
  • First stratum :
  • $F.Y. : N _1=200, n _1=200 \times \frac{2}{100}=4$
  • Ignoring the random numbers greater than $200$ and the repeated numbers, the selected random numbers are: $158 , 092, 009, 200.$
  • Hence, the number of the sample units of sample of $4$ students of First year are: $158, 009, 200.$
  • Second stratum:
  • $S.Y.: N _2=200, n _2=200 \times \frac{2}{100}=4$
  • Ignoring the random numbers greater than $200$ and the repeated numbers. the selected random numbers are : $019,$ $131,057,006$.
  • Hence, the number of the sample units of the sample of $4$ students of $S.Y$. are : $019,131,057,006$.
  • Third stratum:
  • $T.Y. : N_2=200, n_3=200 \times \frac{2}{100}=4$
  • Ignoring the random numbers greater than $200$ and the repeated numbers, the selected random numbers are : $027$ , $070,198,200,058$.
  • Hence, the random number of the sample units of the sample of $4$ students of Third year are : $027, 070, 198, 200.$

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