Question

The accompanying data on cube compressive strength (mpa) of concrete specimens appeared in the article "experimental study of recycled rubber-filled high-strength concrete" (magazine of concrete res., 2009: 549–556): 112.3 97.0 92.7 86.0 102.0 99.2 95.8 103.5 89.0 86.7


a. is it plausible that the compressive strength for this type of concrete is normally distributed

Answer 1

Answer:

The statistical result of analysis of the parameters strongly suggest that compressive stress of the presented type of concrete is normally distributed

Step-by-step explanation:

Here we have

112.3  97.0  92.7  86.0  102.0  99.2 95.8  103.5  89.0  86.7

Mean = 96.42

Standard deviation = 8.26  

Population mean = 100 MPa

Confidence level, α = 0.05

Therefore we have

The hypothesis H₀:  μ= 100 alternative

Hₐ: μ ≠ 100

The test statistic is then

$t=\frac{\bar{x}-\mu }{\frac{\sigma }{\sqrt{n}}}$

Which gives

$t=\frac{96.42-100 }{\frac{8.26 }{\sqrt{10}}}$ = -1.37

Determining the rejection region at α = 0.05

$t<t_{0.05,9} = -1.833$

Therefore, since $t>t_{0.05,9}$ and with the tcdf (-10⁹⁹, -1.37, 9) = 0.102 > α > 0.05

We fail to reject the null hypothesis, and the test is NOT significant

Therefore, by comparison to a normal distributed of distribution, the compressive stress of this type of concrete is normally distributed.