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Solved: The accompanying data on cube compressive strength
Chapter 8, Problem 37E(choose chapter or problem)
Problem 37E
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):
a. Is it plausible that the compressive strength for this type of concrete is normally distributed?
b. Suppose the concrete will be used for a particular application unless there is strong evidence that true average strength is less than 100 MPa. Should the concrete be used? Carry out a test of appropriate hypotheses using the P-value method.
Questions & Answers
QUESTION:
Problem 37E
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):
a. Is it plausible that the compressive strength for this type of concrete is normally distributed?
b. Suppose the concrete will be used for a particular application unless there is strong evidence that true average strength is less than 100 MPa. Should the concrete be used? Carry out a test of appropriate hypotheses using the P-value method.
ANSWER:
Step 1 of 4
Given that,
The data on cube compressive strength (MPa) of concrete specimens is:
112.3 97.0 92.7 86.0 102.0
99.2 95.8 103.5 89.0 86.7
a.
Firstly, plotting the normal probability plot for the data.
All the required calculations are tabulated below:
Location (i) |
Data values (X) |
||
1 |
86.0 |
0.061 |
-1.547 |
2 |
86.7 |
0.1585 |
-1 |
3 |
89.0 |
0.2561 |
-0.655 |
4 |
92.7 |
0.3537 |
-0.375 |
5 |
95.8 |
0.4512 |
-0.123 |
6 |
97.0 |
0.5488 |
0.123 |
7 |
99.2 |
0.6463 |
0.375 |
8 |
102.0 |
0.7439 |
0.655 |
9 |
103.5 |
0.8415 |
1 |
10 |
112.3 |
0.939 |
1.547 |
