Posted: August 26th, 2013

probability and statistics


There are many real-life applications that require the use of descriptive statistics, graphical representations, hypothesis testing, and confidence intervals to make inferences about selected populations.
Suppose that you have been asked to act as a consultant to determine whether or not there is evidence to support an age discrimination lawsuit against a company based on the age of the successful and unsuccessful applicants during a particular year. This task will require you to use selected descriptive statistics and graphical representations, an appropriate hypothesis test, and a confidence interval to make informed decisions and predictions regarding this company.
Refer to the attached “Data Set” to complete this task. You will find two sets of lists (or samples) of ages (in years) of both successful and unsuccessful applicants.
Use the following assumptions:
1. The population standard deviation for each sample is unknown, and no assumption with regard to equality can be made.
2. The samples are independent because values from one sample are in no way matched or paired with the values from the other sample.
3. The two samples are simple random samples.
Task:
A. Describe the procedure used to generate a random integer from 1 to 4 using a random number generator (i.e., what technology/program or method you used to generate it).
• Generate the random number.
1. Let n stand for your random number. Starting with the nth piece of data in each list, use systematic sampling to extract a subset of data from each sample data set, selecting the nth element, and selecting each subsequent nth element in the list until you have run out of data to choose from.
• Copy and then paste each selected subset of data into a table, and submit it as part of your response to this task.
• Make sure that both columns are labeled (i.e., Age_Unsuccessful Applicants, Age_Successful Applicants) for each subset of data.
a. Describe the process you used to generate the subset of data from each sample data set using systematic sampling.
B. Analyze each subset of data, using the selected descriptive statistics described below.
1. Determine the mean, median, and mode (if applicable) of each subset of data, showing all work.
2. Determine the range and standard deviation of each subset of data, showing all work.
3. Summarize all of your results within a table (e.g., the one shown in the attached “Example Results Table”).
4. Analyze the table results to compare each statistic with each subset of data.
C. Since both subsets of data are small, you will need to investigate the extent to which each subset of data comes from a population that has a normal distribution. Your investigation should contain the following components to explore both subsets of data:
1. Construct a histogram for each of the systematic samples you collected.
• Label all axes in an appropriate fashion.
• Using drawing tools, identify the mean, median, and mode (if applicable) that was previously determined.
Note: Copy and paste these graphical representations into a word-processing document (*.rtf) that contains your response to this task.
2. Construct a box plot for each of the systematic samples you collected.
• Label all axes in an appropriate fashion.
• Using drawing tools, identify any outliers, minimum, first quartile, mean, median, third quartile, maximum, and the interquartile range.

Note: Copy and paste these graphical representations into a word-processing document (*.rtf) that contains your response to this task.
3. Discuss the use of all graphical representations to investigate the extent to which each subset of data comes from a normal distribution.
Note: Your results should show trends and patterns that suggest that each subset of data comes from a population with a normal distribution.
D. Perform a hypothesis test using your subsets of data that contains the following components:
1. Describe the null and alternative hypotheses.
Note: Remember that these hypotheses should be expressed in terms of the relevant population means.
Note: Because “The Age Discrimination in Employment Act (ADEA) only forbids age discrimination against people who are age 40 or older” (U.S. Equal Employment Opportunity Commission, n.d.), your hypotheses should only consider age discrimination against older individuals.
2. Discuss what the alpha level represents within the context of the analysis if the significance level is set at ??= 0.05.
3. Justify the hypothesis test that you will use to perform the analysis.
4. Compute an appropriate test statistic, showing all work.
5. Draw a rough sketch of the distribution that you will be working on that includes the critical region, using drawing tools.
• State whether you reject or fail to reject the null hypothesis within the context of the given problem.
6. Provide a discussion where you substantiate your decision to reject or fail to reject the null hypothesis, based on the computed test statistic and identified critical
region.
E. Perform an analysis of your subsets of the data using a 90% confidence level, including the following components:
1. Find the value for the margin of error, showing all work.
2. Find the desired confidence interval, showing all work.
3. Provide an interpretation of these results within the context of the given problem.
F. Incorporate the results that were obtained from each of the previous analyses into a final recommendation for the company to help them make informed decisions and predictions regarding whether or not they need to revise their hiring practices to prevent future possible litigation.
G. If you choose to use outside sources, include all in-text citations and references in APA format.
Note: This task requires you to submit pictures, graphics, and/or diagrams. Each file must be an attachment no larger than 30 MB in size. Diagrams must be original and may be hand-drawn or drawn using a graphics program. Do not use CAD programs because attachments will be too large.
Note: Please submit all graphics and equations in *.pdf (Portable Document Format) files.
Note: Please save word-processing documents as *.rtf (Rich Text Format) files.
Note: When bulleted points are present in the task prompt, the level of detail or support called for in the rubric refers to those bulleted points.
Note: For definitions of terms commonly used in the rubric, see the Rubric Terms web link included in the Evaluation Procedures section.
Note: When using outside sources to support ideas and elements in a paper or project, the submission MUST include APA formatted in-text citations with a corresponding reference list for any direct quotes or paraphrasing. It is not necessary to li
st sources that were consulted if they have not been quoted or paraphrased in the text of the paper or project.

Note: No more than a combined total of 30% of a submission can be directly quoted or closely paraphrased from outside sources, even if cited correctly. For tips on using APA style, please refer to the APA Handout web link included in the APA Guidelines section.
Reference List:
Note: This reference list refers only to direct citations in the task above and may be different from those you need to complete the task. Consult your course of study for a list of suggested learning resources.
U.S. Equal Employment Opportunity Commission. (n.d.). Age Discrimination. Retrieved from http://www.eeoc.gov/laws/types/age.cfm

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