Arithmetic Mean and Five-step P-value Approach

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A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular of 50 packages, the mean amount dispensed is 8.159 ounces, with a sample standard deviation of 0.051
A. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.05 level of significance.)
B. Determine the p-value and
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C. Interpret the meaning of the p-value in (b).
D. Compare your conclusions in (a) and (b).

The U.S. Department of Education reports that 46% of full-time college students are employed while attending college (data extracted from “The Condition of Education 2009,” National Center for Education Statistics, A recent survey of 60 full-time students at Miami University found that 29 were employed.
A. Use the five-step p-value approach to hypothesis testing and a 0.05 level of significance to determine whether the proportion of full-time students at Miami University is different that the national norm of 0.46.
B. Assume that the study found that 36 of the 60 full-time students were employed and repeat (a). Are the conclusions the same?


One of the issues facing organizations is increasing diversity throughout the organization. One of the ways to evaluate an organization’s success at increasing diversity is to compare the percentage of employees in the organization in a particular position with a specific background to the percentage in a position with that specific background in the general workforce. Recently, a large academic medical center determined that 9 of 17 employees in a particular position were female, whereas 55% of the employees for this position in the general workforce were female. At the 0.05 level of significance, is there evidence that the proportion of females in this position at this
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