1. The foundation for a building is designed to rest on 100 piles based on the individual pilecapacity of 80 tons. Nine test piles were driven at random locations into the supporting soil stratumand loaded until failure of each pile occurred. The results are given in Table 1:Table 1 Capacity of each test pileTest Piles Pile Capacity (tons)18227539590458892778885980a. Estimate the mean and standard deviation of the individual pile capacity to be used at thesite.b. At the 5% significance level, should the piles be accepted based on the results of the ninetest piles? That is, perform a one-sided hypothesis test, with the null hypothesis that themean pile capacity is 80 tons.c. Establish the 95% confidence interval for the mean pile capacity, assuming that thestandard deviation of the population is known, o = s.d. Determine the 95% confidence interval for the mean pile capacity in the basis of unknownvariance.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 42 feet. Assume the population standard deviation is 4.7 feet. The mean braking distance for Make B is 45 feet. Assume the population standard deviation is 4.4 feet. At a = 0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. Complete parts (a) rari rz (b) Find the critical value(s) and identify the rejection region(s). The critical value(s) is/are (Round to three decimal places as needed. Use a comma to separate answers as needed.)
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A boat capsized and sank in a lake. Based on an assumption of a mean weight of 142 lb, the boat was rated to carry 60 passengers (so the load limit was 8,520 lb). After the boat sank, the assumed mean weight for similar boats was changed from 142 lb to 171 lb. Complete parts a and b below. a. Assume that a similar boat is loaded with 60 passengers, and assume that the weights of people are normally distributed with a mean of 178.5 lb and a standard deviation of 36.9 lb. Find the probability that the boat is overloaded because the 60 passengers have a mean weight greater than 142 lb. The probability is 1.000. (Round to four decimal places as needed.) C.. b. The boat was later rated to carry only 13 passengers, and the load limit was changed to 2,223 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 171 (so that their total weight is greater than the maximum capacity of 2,223 lb). The probability is. (Round to four decimal…

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