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To check the quality of two brands of li...

To check the quality of two brands of lightbulbs, their life in burning hours was estimated as under for 100 bulbs of each brand.

(i) Which brand gives higher life?
(ii) Which brand is more dependable?

Text Solution

Verified by Experts

Calculation of Mean and Coefficient of Variation

Brand A: `" " barX=A+(sumfdx')/(sumf)xxC`
`=125+(19)/(100)xx50`
=125+9.5=134.5
`sigma_(x)=sqrt((sumfdx'^(2))/(N)-((sumfdx')/(N))^(2))xxC`
`=sqrt((193)/(100)-((19)/(100))^(2))xx50`
`=sqrt(1.93-0.0361)xx50`
`=sqrt(1.8939)xx50`
`=1.38xx500=69`
`CV_(A)=(sigma)/(barX)xx100=(69)/(134.5)xx100=51.3`
Brand B: `" " barX=A+(sumfdx')/(sumf)xxC`
`=125+(23)/(100)xx50`
=125+11.5=136.5
`sigma=sqrt((sumfdx'^(2))/(N)-((sumfdx')/(N))^(2))xxC`
`=sqrt((61)/(100)-((23)/(100))^(2))xx50`
`=sqrt(0.61-0.0529)xx50`
`=sqrt(0.5571)xx50`
`=0.75xx50=37.5`
`CV_(B)=(sigma)/(barX)xx100=(37.5)/(136.5)xx100=27.47`
(i) Brand B gives higher life because average hours of life is more in this case than that of Brand A.
(ii) CV is more in case of Brand A than Brand B , therefore, Brand B is more dependable.]
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