A concrete plant guarantees that the standard deviation of concrete of a specifi

Question

A concrete plant guarantees that the standard deviation of concrete of a specified strength is 250psi. If a construction engineer wants to estimate the mean strength to compression of a delivered batch such that the variance of the sample mean is not greater than 2500 (psi)^2, how many samples should he take from the batch? In problem 10.2, the engineer does not trust the manufacturer recommendation and decides to take a few samples from the batch and test for failure strength with the following results in psi: 3205, 3129, 2847, 3350 2955, 2990, 2833, and 2878. How many more samples should he take? In Problem 10.2, assume that the population standard deviation of concrete strength is indeed 250psi. If the engineer is willing to accept a 5% chance that the margin of error in the mean strength is greater than or equal to 100 psi, estimate the number of samples he needs to collect.

Explanation / Answer

q1:

sample standard dev=sqrt(sample variance)= sqrt(2500) =50

sample standard dev=sqrt(sample mean std dev/n) where n==sample size

50= sqrt(250/n)

(50)^2=250/n

calculating further,n=10

q2. two more data points needed since sample size reuired is 10

q3.

margin of error=5%

n=?

sample std deviation=250

Sample Size = [(Z-score)2 * StdDev*(1-StdDev)] / (margin of error)2

    [ (1.96)^2-(250(1-250)]/(10000)=6

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