Question

The foundation for a building is designed to rest on 100 piles based on the individual pile capacity of 80 tons. Nine test piles were driven into the ground at random locations into the supporting soil stratum and loaded until failure occurred. The following pile capacities (in tons) were determined {80,125,100,110,73,76,79,81,83}

Determine the 99% Confidence Interval for the mean pile capacity assuming that the standard deviation is known; sigma=S

a. {69.6,110}

b. {74.3,105.0}

c. {80.2,91.6}

d. {73.6,120.5}

Answer 1

Solution:

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± Z*σ/sqrt(n)

From given sample, we have

Xbar = 89.6667

σ = S = 17.8885

n = 9

Confidence level = 99%

Critical Z value = 2.5758

(by using z-table)

Confidence interval = Xbar ± Z*σ/sqrt(n)

Confidence interval = 89.6667 ± 2.5758*17.8885/sqrt(9)

Confidence interval = 89.6667 ± 2.5758*5.9628

Confidence interval = 89.6667 ± 15.3592

Lower limit = 89.6667 - 15.3592 = 74.31

Upper limit = 89.6667 + 15.3592 = 105.03

Confidence interval = (74.3, 105.0)

b. {74.3,105.0}