Question

Soil pH is an important variable in the design of structures that will contact the soil. Nine test samples of soil from a potential construction site gave readings of

7.3 6.5 6.4 6.1 6.0 6.5 6.2 5.8 6.7
Assuming that soil pH is normally distributed, find the 90% lower confidence bound for the true average soil pH at the site.

Answer 1

90% lower confidence bound for the true average soil pH at the site is ≈ 6.13

Explanation:

90% Lower Confidence bound can be calculated using M-ME where

• M is the sample mean pH (6.39)

• ME is the margin of error from the mean

And margin of error (ME) can be calculated using the formula

ME=
`(t*s)/(√(N) )` where

• t is the corresponding statistic in the 90% confidence level (1.86)

• s is the standard deviation of the sample PH's (0.42)

• N is the sample size (9)

Using the numbers we get:

ME=
`(1.86*0.42)/(√(9) )` ≈ 0.26

Then the 90% lower confidence bound for the true average soil pH at the site is 6.39 - 0.26 = 6.13