Question

The following statistical information is derived by a sample survey for six villages of mandi district in himachal Pradesh . Are the adoption rates of modern fertilizer and high yielding varieties related to the living standard of the villages?

Respondents classified according to villages and levels of living

	Levels of living scores
Villages	zero	One	two	three	Four	Five	Total cases	Village scores
Sadhiyani	4	6	2	3	3	3	21	2.19
sangroh	7	5	1	4	2	2	21	1.76
munjakhali	5	8	4	---	1	1	19	1.32
dograin	2	11	3	1	1	---	18	1.33
Gagal	13	----	4	1	---	---	18	0.50
longni	8	4	1	---	---	---	13	0.46
Total	39	34	15	9	7	6	110

Tables 32                                                                                       Table 33

Villages –wise analysis of adoption of fertilizers                   Villages –wise analysis of adoption of improved seed

Villages	% of adoption	% adoption before three years		village	Percentage of adoption	% of adoption before three years
Sadhiyani	100	0.0		Sadhiyani	95.3	0.0
sangroh	90.4	5.3		sangroh	95.3	5.0
dograin	83.3	6.6		longni	92.3	25.0
munjakhali	78.9	6.6		dograin	88.8	25.0
longni	69.2	22.2		munjakhali	63.3	8.3
Gagal	50	0.0		Gagal	44.4	0.0

Source : C RAJAGOPALAN AND JASPAL SINGH. ADOPTION OF AGRICULTURAL INNOVATION DELHI; NATIONAL PUBLISHING HOUSE 1971

Answer 1

Solution

Let x = living standard score; y = Increase in percentage adoption of fertilizer

z = Increase in percentage adoption of improved seed

The correlation coefficient between x and y = r_xy = 0.99943

The correlation coefficient between x and z = r_xz = 0.9552

Both correlation coefficients are very high.

So, there is evidence to suggest that the adoption rates of modern fertilizer and high yielding varieties related to the living standard of the villages. ANSWER

Values of x, y and z are given in the table below:

Village	Living Standard Score	Increase in percentage adoption of fertilizer	Increase in percentage adoption of improved seed
Sadhiyani	2.19	100	95.3
sangroh	1.76	85.1	90.3
munjakhali	1.32	76.7	67.3
dograin	1.33	72.3	63.8
Gagal	0.5	47	55
longni	0.46	50	44.4