(Solution) - A Explain why use of the z statistic is appropriate -(2025 Original AI-Free Solution)

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a. Explain why use of the z statistic is appropriate in this setting.
b. Describe Type I and Type II errors in this context.
c. The rejection of H0 when z ? 1.8 corresponds to what value of a? (That is, what is the area under the z curve to the right of 1.8?)
d. Suppose that the actual value for µ is 153 and that H0 is to be rejected if z ? 1.8. Draw a sketch (similar to that of Figure 10.5) of the sampling distribution of x, and shade the region that would represent b, the probability of making a Type II error.
e. For the hypotheses and test procedure described, compute the value of b when µ = 153.
f. For the hypotheses and test procedure described, what is the value of b if µ = 160?