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Question 1: There are 180 primary schools in a country area having an average of 30...

Question 1:

There are 180 primary schools in a country area having an average of 30 or more people under the age of 21 per class. A sample of 30 schools drawn using systematic sampling with an interval of k = 6.

Serial number

1

2

3

4

5

6

   7

8

9

10

No. of students

60

200

45

50

40

79

35

41

30

120

Serial number

11

12

13

14

15

16

17

18

19

20

No. of students

300

65

111

120

200

42

51

67

32

40

Serial number

21

22

23

24

25

26

27

28

29

30

No. of students

46

55

250

100

63

90

47

82

31

50

  1. Estimate total number of students.
  2. Estimate average number of students per farm.
  3. The variance of the sample mean of students per farm.
  4. 95% confidence interval for the total number of students.

Solutions

Expert Solution

There are 180 primary schools in a country area having an average of 30 or more people under the age of 21 per class. A sample of 30 schools drawn using systematic sampling with an interval of k = 6.

Serial number 1 2 3 4 5 6    7 8 9 10 Total
No. of students 60 200 45 50 40 79 35 41 30 120 700
Serial number 11 12 13 14 15 16 17 18 19 20
No. of students 300 65 111 120 200 42 51 67 32 40 1028
Serial number 21 22 23 24 25 26 27 28 29 30
No. of students 46 55 250 100 63 90 47 82 31 50 814
2542

First let us denote the sample data set by the letter

  1. Estimate total number of students.

Ans.

  

  1. Estimate average number of students per farm.

Ans.

  1. The variance of the sample mean of students per farm.

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