Question

Problem 4. The foundation of a building is designed to rest on 100 piles based on the individual pile capacity of 80 tons. Nine test piles were driven at random locations into supporting soil stratum and loaded until failure of each pile occurred. The results are as follows: Test pile Pile Capacity (tons) a) Estimate the mean and standard deviation of the individual pile capacity to be used at the b) c) d) 82 75 95 90 8892 78 85 80 site. At the 5% significance level, should the piles be accepted based on the results of the nine test piles? Explain. Establish the 99% confidence interval for the mean pile capacity, assuming that the standard deviation of the population is known ơ Determine the 99% confidence interval for the mean pile capacity on the basis of unknown s

Answer 1

Data given in the problem and solution

• No of test piles driven = 9
• Piles capacity recorded in tons as 82,75,95,90,88,92,78,85,80 respectively

Since the no of sample is small and the variation is not known, the statistic follows t – distribution with mean μ and standard deviation is s/ square root of N, then,
t=2.22  

• Sample standard deviation is 6.76 tons
• Sample mean is 85 tons

        The above t value is obtained by the t distribution formula

     $t= x-\upsilon /\sigma /\eta$

               t Value is corresponding to 5 % significance level (for one test) is 1.8595.

• since the tested piles significance level is 1.8595 at 5 percent . it can be acceptable value
• but it is not accurate to follow therefore based on situation we can follow this criteria