Concrete placed on a structure was subsequently cored after 28 days, and the fol

Question

Concrete placed on a structure was subsequently cored after 28 days, and the following results were obtained of the compressive strengths from five test specimens: 4042, 3505, 3402, 3939, 3472 psi (a) Determine the 90% two-sided confidence interval of the mean concrete strength. (b) Suppose the confidence interval established in part (a) is too wide, and the engineer would like to haw a confidence interval to be plusminus 300 psi of the computed sample mean concrete strength. Generally, more specimens of concrete would be needed to keep the same confidence level. However, without additional samples, what is the confidence level associated with the specified interval based on the five measurements given above? (c) If the required minimum compressive strength is 3500 psi, test whether the concrete satisfies these requirements by performing a one-sided hypothesis test at the 2% significance level.

Explanation / Answer

Below are the mean and standard deviation for the given data

(a) For 90% CI, t-value = 2.13

lower bound = mean - t*sigma/sqrt(n) = 3672 - 2.13*264.19/sqrt(5) = 3420.342

upper bound = mean + t*sigma/sqrt(n) = 3672 + 2.13*264.19/sqrt(5) = 3923.658

(b)

ME = t*sigma/sqrt(n)

t = 300*sqrt(5)/264.19 = 2.54

This t-value is equivalent to 93.6% Confidence interval.

(c)

test statistics t = (3672 - 3500)/(264.19/sqrt(5)) = 1.455

p-value = 0.1096

As p-value is greater than significance level of 0.02, we reject the null hypothesis.

This means there are not enough evidence to conclude that the compressive strength is greater than 3500.

mean 3672 std. dev. 264.1886

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