Concrete admixtures are natural or manufactured chemicals added during concrete mixing to enhance specific properties of

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Concrete admixtures are natural or manufactured chemicals added
during concrete mixing to enhance specific properties of the fresh
or hardened concrete, such as workability, durability, or early and
final strength. Two admixtures are being tested to determine how
they affect the strength of the concrete. Both admixtures are in
use but admixture 2 is cheaper and it should be adopted provided
that it does not affect the compressive strength of the concrete. A
test was conducted in the laboratory and the results are shown
in the table. Assume that the strengths are normally distributed
with the same standard deviation. Use α = 0.05
1. What is the standard deviation for each sample?
2. Provide appropriate null and alternative hypothesis.
3. Provide appropriate rejection criteria.
4. Determine if there is any difference to the compressive
strength of the concrete (provide and interpret your
conclusion).
5. Find a 95% confidence interval on the difference in means for
the two observations.