Concrete testing A company that specializes in developing concrete for construction strives to continually improve the properties of its materials In order to increase the compressive strength of one of its new formulations, they varied the amount of alkali content (low, medium, high) Since the type of sand used may also affect the strength of concrete, they used three different types of sand (Types I, II, III) Four samples were randomly selected from each treatment combination to be tested The boxplots show the test results on compressive strength (in psi) for the three levels of alkali content and three types of sand Two way ANOVA results are also given a) Is this an experiment or an observational study Explain b) Are the conditions for two way ANOVA met c) If so, perform the hypothesis tests and state your conclusions in terms of compressive strength, alkali content, and sand type d) Is it appropriate to interpret the main effects in this case Explain Strength (psi) Strength (psi) 3600 3400 3200 3000 2800 2600 2400 2200 2000 H 3600 3400 3200 3000 2800 2600 2400 2200 2000 L Alkali Content III Sand Type Sum of Mean M Source DF Squares Square F ratio P value Alkali Content 2 4016600 2008300 46 38 0 000 Sand Type Interaction Error Total 2 1547817 773908 17 87 0 000 4 177533 44383 1 02 0 412 27 1169250 43306 35 6911200

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Concrete testing. A company that specializes in developing concrete for construction strives to continually improve the properties of its materials. In order to increase the

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Concrete testing. A company that specializes in developing concrete for construction strives to continually improve the properties of its materials. In order to increase the compressive strength of one of its new formulations, they varied the amount of alkali content (low, medium, high). Since the type of sand used may also affect the strength of concrete, they used three different types of sand (Types I, II, III). Four samples were randomly selected from each treatment combination to be tested. The boxplots show the test results on compressive strength (in psi) for the three levels of alkali content and three types of sand. Two-way ANOVA results are also given.

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a) Is this an experiment or an observational study? Explain.

b) Are the conditions for two-way ANOVA met?

c) If so, perform the hypothesis tests and state your conclusions in terms of compressive strength, alkali content, and sand type.

d) Is it appropriate to interpret the main effects in this case? Explain.

Strength (psi) Strength (psi) 3600 3400 3200 3000 2800 2600 2400 2200 2000 H 3600 3400 3200 3000 2800 2600 2400 2200 2000 L Alkali Content III Sand Type Sum of Mean M Source DF Squares Square F-ratio P-value Alkali Content 2 4016600 2008300 46.38 0.000 Sand Type Interaction Error Total 2 1547817 773908 17.87 0.000 4 177533 44383 1.02 0.412 27 1169250 43306 35 6911200