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The water content of a soil volume is measured four times gravimetrically by oven drying. The mean value of the water content is 23.2%. If the standard deviation of the four measurements is 1.0%, the 99% confidence interval for the soil water content is most nearly:________.
A. (19.5%, 26.9%)
B. (18.6%, 27.8%)
C. (20.6%, 25.8%)
D. (20.9%, 25.5%)

Respuesta :

99% confidence interval for soil water content is  approx : A (19.5%, 26.9%)

Given : Mean x' = 23.2% = 0.232 , Standard Deviation s = 1% = 0.01 , Confidence Limit = 99%

Confidence Internal = x' + t ( s / √n)

t at 99% confidence limit, ie 1% ( 0.01 ) critical value  

t at 0.01/ 2, for two sided = t 0.005 = 7.4534

0.232 +  7.4534 ( 0.01 / √4 )

= 0.232 + 0.03736

= ( 0.232 + 0.03736 , 0.232 - 0.03736 )

= 0.19474 , 0.26926

= 19.5% , 26.9%

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