Concept explainers
Before you solve each problem below, first categorize it by answering the following question: Are we testing a single mean or a single proportion? Assume underlying population distributions are mound-shaped and symmetric for problems with small samples that involve testing a mean. Then provide the following information for Problems 7-14.
(a) What is the level of significance? State the null and alternate hypotheses.
(b) Check Requirements What sampling distribution will you use? What assumptions are you making? Compute the sample test statistic and corresponding distribution value.
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level
(e) Interpret your conclusion in the context of the application.
Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more “conservative” answer. Answers may vary due to rounding.
Civil Service: College Degrees The U.S. Office of Personnel Management reports that 51% of federal civilian employees have a bachelor's degree or higher (OPM.gov). A random sample of 100 employees in the private sector showed that 41 have a bachelor’s degree or higher. Does this indicate that the percentage of employees holding bachelor's degrees or higher in the private sector is less than that in the federal civilian sector? Use
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Understanding Basic Statistics
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