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Exercise A-1 A home builder is testing concrete compressive strength in a particular batch in advance of an upcoming housing development. Under the null hypothesis, the mean strength is at least 3000psi as advertised by the concrete manufacturer. Of course, the builder will have a problem on their hands if the concrete tests at significantly less than that. Assume that the strengths are normally distributed with population standard deviation of 500 psi. (a) State the null and alternative hypotheses of the builder's test. Given a sample of size 10, define a rejection region in terms of mean strength, X, under the one-sided alternative hypothesis at significance level a= 0.05. (b) Based on the result from part a, calculate the power of the test at the alternative true mean strengths of 2600 psi. Explain this value in the context of the problem. (c) Based on the result from part a, what is the probability of a Type IJ error when the true mean compressive strength is 2600psi? Explain this value in the context of the