Question

Soil samples from nine locations at a site are taken to determine the bearing capacity in kN/m^2. The results are summarized:

23.1, 42.4, 30.3, 31.0, 28.4, 39.3, 32.4, 27.4, 38.0

(a) Estimate the mean, standard deviation, and COV of the data

(b) Compute the standard error of the mean.

(c) Establish 95 percent confidence intervals for the mean.

(d) Using the COV from (a) how many samples must be tested to have +/- 10 percent error for the mean at 95 percent confidence?

Answer 1

(a)

(i)

Mean () is given by:

(ii)

x	x -	(x - )2
23.1	- 9.3778	87.9427
42.4	9.9222	98.4505
30.3	- 2.1778	4.7427
31.0	- 1.4778	2.1838
28.4	- 4.0778	16.6283
39.3	6.8222	46.5427
32.4	- 0.0778	0.0060
27.4	- 5.0778	25.7838
38.0	5.5222	30.4949
Total =		312.7756

Standard Deviation (s) is given by:

(iii)

Coefficient of Variation (CV) is given by:

%

(b)

Standard Error f Man is given by:

(c)

= 0.05

ndf = 9 - 1 = 8

From Table, critical values of t = 2.3060

Confidence Interval:

32.4778 (2.3060 X 2.0843)

= 32.4778 4.8063

= (27.6715 , 37.2841)

Confidence Interval:

27.6715 < < 37.2841

(d)

Number of samples (n) is given by:

Given:

= 0.05

From Table, critical values of Z = 1.96

= 6.2528

e = 0.10

Substituting we get:

So,

Answer is:

25