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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.

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Answer:

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

Step-by-step 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=[tex]\frac{t*s}{\sqrt{N} }[/tex] 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=[tex]\frac{1.86*0.42}{\sqrt{9} }[/tex] ≈ 0.26

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

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