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random sample of 24 Mason students was collected and each student was asked

INSTRUCTIONS TO CANDIDATES
ANSWER ALL QUESTIONS

Your solutions document should include the following items.  Points will be deducted if the following are not included. 

Please note: all StatKey or Rguroo Instructions provided in the parts of the problems will be presented in italics.

Elements of good technical writing:

Use complete and coherent sentences to answer the questions.

Graphs must be appropriately titled and should refer to the context of the question.

Graphical displays must include labels with units if appropriate for each axis.

Units should always be included when referring to numerical values.

When making a comparison you must use comparative language, such as “greater than”, “less than”, or “about the same as.”

Ensure that all graphs and tables appear on one page and are not split across two pages.

Type all mathematical calculations when directed to compute an answer ‘by-hand.’ 

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When writing mathematical expressions into your solutions document you may use either an equation editor or common shortcuts. For example, √x can be written as sqrt(x), p ̂ can be written as p-hat, and x ̅ can be written as x-bar.

 

Investigation 1: Appropriateness of Inference: Price of a Haircut

For the following scenario, answer the questions below.  Please note, do not conduct inference in this problem; just answer each question.

 

A random sample of 24 Mason students was collected and each student was asked, among other things, the total cost of their last hair service (including cuts, styling, etc.).  The researcher does not have any information about the population from which the sample was collected.  The data set is called HairPrice.  

 

If we attempt to conduct statistical inference using the collected sample, what is the parameter of interest?  Use the correct symbol and describe the parameter in context in one sentence.

 

Check the specific conditions necessary to consider conducting inference using theory-based methods using the t-distribution.  There are three to consider: (1) Was a random sample collected; (2) Is the population where the sample comes from normal; and (3) Is the sample size greater than or equal to 30?  Answer each of these questions in one sentence.

 

What could be checked using the sample data if our sample size is less than 30?  Answer this question in one sentence.

 

Depending on your answer to part (a), construct one or two frequency histograms in Rguroo.  Remember to properly title and label the graph(s).  Copy and paste this graph (or these graphs) into your document.

 

Describe the shape of the histogram(s) in one sentence.

 

Depending on your answer to part (a), construct one or two horizontal boxplots in Rguroo.  Remember to properly title and label the graph(s).  Copy and paste this graph (or these graphs) into your document.

 

Does the boxplot (or do the boxplots) show any outliers?  Answer this question in one sentence and identify any outliers if they are present.

 

Considering your answers to parts (e) and (g), is theory-based inference appropriate in this case?  If you respond “yes,” provide a reason for your response.  If you respond “no,” state the reason why not and present another possibility if the researcher still wanted to conduct statistical inference.  Use one or two complete sentences in your response.

 

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