Question

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%)

Answer 1

Answer:

99% confidence interval for the soil water content is determined by

(0.19474, 0.26926)

Step-by-step explanation:

Explanation:-

Given mean of the sample = 23.2% = 0.232

Given standard deviation of the sample = 1.0% =0.01

Given sample size 'n' =4

Degrees of freedom = n-1 =4-1 =3

critical value = 0.01

$t_{\frac{0.01}{2} } = t_{0.005} =7.4534$

99% confidence interval for the soil water content is determined by

$((x^{-} - t_{0.005} \frac{S.D}{\sqrt{n} } , (x^{-} + t_{0.005} \frac{S.D}{\sqrt{n} })$

$((0.232 - 7.4534\frac{0.01}{\sqrt{4} } , (0.232 + 7.4534 \frac{0.01}{\sqrt{4} })$

( 0.232 -0.03726 , 0.232 +0.03726)

(0.19474, 0.26926)

Final answer:-

99% confidence interval for the soil water content is determined by

(0.19474, 0.26926)