Perform a Hypothesis Test for the Population Mean $$\begin{array} { l } \mathrm { H } _ { 0 } : \mu = \mu _ { 0 } \\ \mathrm { H } _ { \mathrm { a } } : \mu < \mu _ { 0 } \end{array}$$

question 47

Essay

Perform a hypothesis test for the population mean. Assume that preliminary data analyses indicate that it is reasonable to apply the z-test. Use the critical-value approach.
-A hypothesis test for a population mean is conducted. The hypotheses are: $$\begin{array} { l } \mathrm { H } _ { 0 } : \mu = \mu _ { 0 } \\ \mathrm { H } _ { \mathrm { a } } : \mu < \mu _ { 0 } \end{array}$$ The significance level is 0.08 and the critical value is -1.41. Sketch a normal curve displaying the decision criterion. This curve will represent the normal curve for the test statistic under the assumption that the null hypothesis is true. On your graph indicate the area in the tail, the critical value, the rejection region, and the nonrejection region.

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Definitions:

Direct Labor Rate Variance

The difference between the actual cost of labor per hour and the standard or expected cost, multiplied by the total labor hours worked.

Direct Labor Time Variance

The difference between the actual labor time spent on a product and the standard labor time expected, affecting product costs.

Standard Costs

Predetermined or estimated costs that are used as benchmarks for measuring the performance of actual costs in manufacturing or production.

Actual Costs

Actual costs are the real or true costs incurred for materials, labor, and overhead in the production of goods or provision of services, as opposed to estimated or standard costs.