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 Observation Number Admixture 1 Admixture 2
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
| Observation Number | Admixture 1 | Admixture 2 |
| 1 | 23.2 | 23.5 |
| 2 | 25.1 | 20.1 |
| 3 | 24.5 | 22.2 |
| 4 | 23.7 | 20.7 |
| 5 | 23.3 | 21.9 |
| 6 | 24.4 | 25.0 |
| 7 | 22.5 | 22.7 |
| 8 | 24.6 | 20.3 |
| 9 | 25.0 | 22.8 |
| 10 | 24.3 | 22.9 |
| 11 | 24.1 | 21.1 |
| 12 | 24.1 | 22.3 |
| 13 | 25.0 | 21.6 |
| 14 | 24.6 | 20.8 |
| 15 | 22.1 | 22.0 |
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.
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