Section B Q1. Calculate the coefficient of correlation by Scatter diagram (bi-variate table ) from the data given below: Score in the subject X 20-21 Class 12-13 14-15 16-17 18-19 22-23 24-25 Total interval 35-37 1 1 2 32-34 3 9 29-31 1 8 1 18 26-28 4 4 11 4 1 30 23-25 2 1 4 1 19 20-22 3 2 1 1 7 Total 5 8 13 18 30 9. 85 Also give the interpretation. Q2. A group of 20 students were given an achievement test under two conditions: (i) when tense (ii) when relaxed. Test the significance of the difference between means at .05 level on the basis of the following data: Roll No. Score when Score when Roll No. Score when Score when tense relaxed tense relaxed 1 18 20 11 10 10 16 22 12 12 18 24 13 20 22 4 12 10 14 12 14 5 20 25 15 16 12 6. 17 19 16 16 20 7 18 20 17 18 22 8. 20 21 18 20 24 9. 22 23 19 18 23 10 20 20 20 21 17

Section B Q1. Calculate the coefficient of correlation by Scatter diagram (bi-variate table ) from the data given below: Score in the subject X 20-21 Class 12-13 14-15 16-17 18-19 22-23 24-25 Total interval 35-37 1 1 2 32-34 3 9 29-31 1 8 1 18 26-28 4 4 11 4 1 30 23-25 2 1 4 1 19 20-22 3 2 1 1 7 Total 5 8 13 18 30 9. 85 Also give the interpretation. Q2. A group of 20 students were given an achievement test under two conditions: (i) when tense (ii) when relaxed. Test the significance of the difference between means at .05 level on the basis of the following data: Roll No. Score when Score when Roll No. Score when Score when tense relaxed tense relaxed 1 18 20 11 10 10 16 22 12 12 18 24 13 20 22 4 12 10 14 12 14 5 20 25 15 16 12 6. 17 19 16 16 20 7 18 20 17 18 22 8. 20 21 18 20 24 9. 22 23 19 18 23 10 20 20 20 21 17

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 24PFA

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Question

Section B
Q1. Calculate the coefficient of correlation by Scatter diagram (bi-variate table ) from the data
given below:
Score in the subject X
20-21
Class
12-13
14-15
16-17
18-19
22-23
24-25
Total
interval
35-37
1
1
2
32-34
3
9
29-31
1
8
1
18
26-28
4
4
11
4
1
30
23-25
2
1
4
1
19
20-22
3
2
1
1
7
Total
5
8
13
18
30
9.
85
Also give the interpretation.
Q2. A group of 20 students were given an achievement test under two conditions: (i) when tense
(ii) when relaxed. Test the significance of the difference between means at .05 level on the basis
of the following data:
Roll No.
Score when Score when Roll No.
Score when Score when
tense
relaxed
tense
relaxed
1
18
20
11
10
10
16
22
12
12
18
24
13
20
22
4
12
10
14
12
14
5
20
25
15
16
12
6.
17
19
16
16
20
7
18
20
17
18
22
8.
20
21
18
20
24
9.
22
23
19
18
23
10
20
20
20
21
17

Expert Solution

Step 1

“Since you have posted multiple questions, we will provide the solution
only to the first question as per our Q&A guidelines. Please repost the
remaining questions separately.”

Given information:

The bi-variate table is given.

Step 2

The table below shows the values of the mid-points for both row and column class intervals, $m_{y} a n d m_{x}$ , and the values of $d_{x}, d_{y}, f d_{x}, f d_{y}, f {d_{x}}^{2}, a n d f {d_{y}}^{2}$ .

		scores in x
class interval	12-13	14-15	16-17	18-19	20-21	22-23	24-25	Total $(f_{y})$	$m_{y}$	$d_{y} = \frac{m_{y} - A}{h}$	$f d_{y}$	$f {d_{y}}^{2}$
35-37					1		1	2	36	3	6	18
32-34					6	3		9	33	1.5	13.5	20.25
29-31		1	2	6	8	1		18	30=A	0	0	0
26-28		4	4	6	11	4	1	30	27	-1.5	-45	67.5
23-25	2	1	6	5	4	1		19	24	-3	-57	171
20-22	3	2	1	1				7	21	-4.5	-31.5	141.75
Total $(f_{x})$	5	8	13	18	30	9	2	$N = 85$		$\sum_{} d_{y} = - 4.5$	$\sum_{} f d_{y} = - 114$	$\sum_{} f {d_{y}}^{2} = 418.5$
$m_{x}$	12.5	14.5	16.5	18.5=B	20.5	22.5	24.5
$d_{x} = \frac{m_{x} - B}{h}$	-3	-2	-1	0	1	2	3	$\sum_{} d_{x} = 0$
$f d_{x}$	-15	-16	-13	0	30	18	6	$\sum_{} f d_{x} = 10$
$f {d_{x}}^{2}$	45	32	13	0	30	36	18	$\underset{}{\sum f {d_{x}}^{2} = 174}$