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 3psi as advertised by the concrete manufacturer. Elf 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 50D psi. {a} State the null and alternative hypotheses of the builder's test Given a sample of size It}. dene a rejection region in terms of mean strength if, under the onesided alternative hypothesis at signicance level or: CLUE. [b] Based on the result from part a, calculate the power of the test at the alternative true mean strengths of Z 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 II error when the true mean compressive strength is Eopsi? Explain this value in the context of the