Question

A community college employs 89full lime faculty members. To gain the faculty's opinions about an upcoming building project, the college president wishes to obtain a simple random sample that will consist of 9 faculty members. He numbers the faculty from 1 to 89. Complete parts (a) and (b) below. 

Click the icon to view the random number table. 

 (a) Using the provided random number table, the president closes his eyes and drops his ink pen on the table. It points to the digit in row 3, column 6. Using this position as the starting point and proceeding downward, determine the numbers for the 9 faculty members who will be included in the sample. 

The numbers for the faculty members are (Use a comma to separate answers as needed.) 

(b) The president uses technology to produce the following random numbers.

 87 16 54 48 64 16 25 29 31 37

 Determine the numbers for 9 faculty members who will be included in the sample.

 The numbers for the faculty members are _______ 

 

Answer 1

Ans:

The number in 3rd row and 6th column is 9

Select 9 sets of 2 random numbers from this starting point towards downword = (9,4), (4,9), (4,4), (4,7), (8,6), (2,4), (5,2), (9,3), (2,5)

In the random number set use first number in 10th place and second number in 1th place to make a two digit percentage value

So, respective percentages will be 94%, 49%, 44%, 47%, 86%, 24%, 52%, 93%, 25%

Since, none of the above percentage are repeating so, select the faculty members w.r.t the percentile values (Non-replacement technique or Percentile method):

0.94*89 = 83.66 or 84th number = 84

0.49*88 = 43.12 or 43rd number = 43

.44*87 = 38.28 or 38th number = 38

.47*86 = 40.42 or 40th number = 41 (Already 38 has selected which is less than 40. Now, all the number above 38 have shifted 1 position towards down. So, 41 shifted to 40th position)

0.86*85 = 73.1 or 73th number = 76 (38, 41, and 43 selected so, all the numbers above 43 have shifted 3 steps downword)

0.24*84 = 20.16 or 20th number = 20 (No number selected till now below 20 so the position of all the numbers below 20 has not changed)  

0.52*83 = 43.16 or 43rd number = 47 (20, 38, 41, 43 has selected)

0.93*82 = 76.26 or 76th number = 82 (6 numbers below 76 has selected)

0.25*81 = 20.25 or 20th number = 21

Therefore the selected faculty members are 84, 43, 38, 41, 76, 20, 47, 82 and 21

b.

The selected random numbers are 87, 16, 54, 48, 64, 16, 25, 29, 31, and 37

The above random number are selected from the range value of 0 to 99

In point 'a' the faculty numbers are selected using replacement technique

Let's select the faculty using non-replecement technique or percentile method

87 percentile data point in 89 numbers = 0.87*89 = 77.43 or 77th number = 77

16 percentile data point in 88 numbers = 0.16*88 = 14.08 or 14th number = 14

54 percentile data point in 87 numbers = 0.54*87 = 44.98 or 45th number = 46 (Already 14 is selected which was in 14th position. So, all the above 14 numbers are decreased by one step. Therefore the 46 number shifted to 45th position)  

48 percentile data point in 86 numbers = 0.48*86 = 41.28 or 41th number = 42  

64 percentile data point in 85 numbers = 0.64*85 = 54.4 or 54th number = 57 (14, 46 and 42 are selected so the numbers above 46 decreased by 3 positions)

16 percentile data point in 84 numbers = 0.16*84 = 13.44 or 13th number = 13 (No number selected below 13 so position of all the numbers below 14 has not changed)

25 percentile data point in 83 numbers = 0.25*83 = 20.75 or 21th number = 23 (13 and 14 has selected)

29 percentile data point in 82 numbers = 0.29*82 = 23.78 or 24th number = 27 (13, 14, 23 have selected)

31 percentile data point in 81 numbers = 0.31*81 = 25.11 or 25th number = 28 (13, 14, 23 have selected)

37 percentile data point in 80 numbers = 0.37*80 = 29.6 or 30th number = 35 (13, 14, 23, 27,28 have selected

Therefore the selected faculty members are 77, 14, 46, 42, 57, 13, 23, 27, 28, 35

Answer 2