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प्रश्न
Find the number of pairs of observations from the following data,
r = 0.15, `sigma_"y"` = 4, `sum("x"_"i" - bar"x")("y"_"i" - bar"y")` = 12, `sum("x"_"i" - bar"x")^2` = 40.
उत्तर
Given, r = 0.15, `sigma_"y"` = 4, `sum("x"_"i" - bar"x")("y"_"i" - bar"y") `= 12, `sum("x"_"i" - bar"x")^2` = 40
Since, `sigma_"x" = sqrt(1/"n" sum("x"_"i" - bar"x")^2) = sqrt(40/"n"`
Cov (x, y) = `1/"n" sum("x"_"i" - bar"x")("y"_"i" - bar"y")`
= `1/"n" xx 12`
∴ Cov (x, y) = `12/"n"`
Since, r = `("Cov (x, y)")/(sigma_"x" sigma_"y")`
∴ 0.15 = `(12/"n")/(sqrt(40/"n") xx 4)`
∴ 0.15 = `3/("n" xx sqrt(40/"n")`
∴ 0.15 = `1/(sqrt("n") xx sqrt(40)`
Squaring on both the sides, we get
0.0025 = `1/("n" xx 40)`
∴ n = `1/(0.0025 xx 40)`
= `10000/(25 xx 40)`
= `10000/1000`
∴ n = 10
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