Writing Intensive Statistics Course

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Writing Intensive Statistics Course

• Dr. Renan Sezer
• LaGuardia Community College

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Why Write?

• Write to learn
• Improve communication skills
• Develop analytical reading ability
• Develop ability to interpret result
• Frequent feedback

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Writing Exercises

• Low stake writing assignments
• Lead Up or Follow Up
• Staged high stake writing assignments

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Outcomes

• Better understanding of the concepts
• Higher success rate on exams
• Increased teacher-student interaction
• Improved writing
• Reduced fear of writing

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What did the students say?

• 77 - helpful in learning the subject better
• 85 - helped better prepare for the exam
• 69 - recommend such course for future students
• 15 - not sure
• 15 - not recommend

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Writing Assignment I (Week 1)

• A small company pays its president 200,000. The
  vice-president gets 150,000. The foreman earns
  30,000. There are three workers in the company,
  earning 25,000, 22,000, 22,000 respectively.
  The secretary earns 19,000.

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1. Find the mode, median, mean income in this
   company.
2. The union representative wants to negotiate new
   wages. In this negotiation would he emphasize
   mode, median or mean? Explain why in a
   paragraph.
3. Which of the three measures would the president
   of the company stress in the negotiations?
   Explain why in a paragraph.
4. Which do you think best represents this sample?
   Explain why in a paragraph.
5. Can you say that the measure you chose in 4 is
   always best to use? Explain why or why not in a
   paragraph.

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A Mediocre One

• 1)
• Mode 22,000 (appears twice)
• 19,000, 22,000, 22,000, 25,000, 30,000,
  150,000, 200,000
• Mean 468,000 / 7 66,857
• Median 19t, 22t, 22t, 25t, 30t, 150t, 200t
• 2) I think that the union representative would
  want to base his petition on the mode salary.

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• By doing this, using the mode, he can argue
  that the three workers and the secretary are
  underpaid.
• 3) ? (I have no idea) but as a president of a
  company I would be primarily concerned in the
  companys profits and not increasing my
  employees wages. I would stress the mean since
  it a higher number than the median or mode.
• 4) Median is best choice. I think that the mean
  (66,857) wage is not a true representation of
  the individual wages since there are such large

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• discrepancies among them, but then neither is
  the mode or the median. There is no best
  representation.
• 5) Since I feel that neither mean, mode or median
  are of any use to best represent this sample the
  best choice would depend on job descriptions and
  their respective hourly wages.
• My answer probably makes no sense but neither
  does this problem since union and management are
  usually at odds when it comes

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• to coming to common ground when the problem is
  about employee demands and especially wages. The
  union wants better wages and working conditions
  while management is concerned about production
  and profit margin. I do not feel that this
  approach of using mean, mode and median will help
  to solve the problem.

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A Bad One

• 1) a) Mode is 22,000
• b) Mean is 3319714.2
• The sam of all wages divited by 7
• 23238000 / 7 3319714.2
• c) Median is 25000
• 2) The union representative who wants to
  negotiate new wages has to emphazize

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• the median of that company. He has to compare
  it with the standarts given by the graph. By
  doing so, he can show that the median of the
  company is far less than the standarst.
• 3) The president of the company would stress in
  the negotiations on the Mode because it is close
  to the standarts given in the graph.
• 4) Median represents best this sample.

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• 5) The measure that I chosed in this sample is
  Median But, that doesnt mean that it is always
  the best to use because it is not going to be
  fair in other circumstances. Some times is
  better to use Mean.

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Writing Assignment II (Week 2)

• Describe in your own words what mean and standard
  deviation indicate. Give examples. (Note You
  are not asked to describe how mean and standard
  deviation are calculated.)

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Writing Assignment III (Week 3)

• Drug X has standard deviation of 3 days recovery
  time. Drug Y has standard deviation of 7 days
  recovery time. Based solely on this information
  which of the following statements is true?
• a) Drug X is a better drug than drug Y.
• b) Drug Y is a better drug than drug X.
• c) Drug X and drug Y are equally good.
• d) No decision can be made.
• Given the standard deviation above, suppose drug
  X has mean recovery time of 30 days and drug Y
  has mean recovery time of 15 days. Explain which
  drug is better.

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• Given the standard deviation above, suppose drug
  X has mean recovery time of 8 days and drug Y has
  mean recovery time of 20 days. Explain which
  drug is better.
• Looking back on your answers to previous
  questions, write a paragraph about reaching a
  decision based solely on standard deviation.

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Writing Assignment IV (Week 4)

• Explain in your own words what it means for two
  events to be independent. (You are not asked to
  give a formula.) Give an example.
• Explain in your own words what it means for two
  events to be dependent. (You are not asked to
  give a formula.) Give an example.
• Explain in your own words what it means for two
  events to be mutually exclusive. Be sure to use
  the concepts of dependence and independence,
  which you have used in part A, and B, in
  explaining mutually exclusive events. Give an
  example.

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Writing Assignment V (Week 7) 

• It is impossible to set up a table giving areas
  of regions lying beneath normal curves for each
  different pair of means, ?, and standard
  deviations, ?. Clearly one way to get around
  this problem is to standardize the distribution
  so that we can work with a normal curve having
  mean 0, and standard deviation 1. Then, a single
  table will be sufficient to estimate areas.
•  

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• Suppose that Tom and Diane are enrolled in two
  different sections of a statistics class. Assume
  a sufficiently large class size, so that the
  scores on the first exam follow a normal
  distribution. In Toms section, the average is
  60 and his score is 72. In Dianes section, the
  average is 71 and her score is 83. Both are
  happy because their scores are 12 points above
  the average of each respective section. Who did
  better and why?

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• Suppose that the standard deviations in Dianes
  section was ?6.4 and in Toms section was ?6.5.
  Now who did better and why?
•  
• Find Dianes percentile and Toms percentile.

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Writing Assignment VI (Week 8) 

• Often in real life it is almost impossible to
  find the mean of a large population.
• A)   If you were a statistician and needed to
  find the mean of a large population, what could
  you do to estimate the population mean?

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• B)   Does the method that you describe in part A
  take into consideration the possible occurrence
  of great numbers of outliers?
• C)    How might you modify or extend the method
  you describe in part A to reduce the influence of
  outliers on your estimate of the mean.

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Writing Assignment VII (Week 9)

• Describe in your own words the (celebrated)
  Central Limit Theorem. What assumptions must be
  met in order to use its conclusions? Give an
  example of a situation where the Central Limit
  theorem may fail because of unmet assumptions

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Writing Assignment VIII (Week 10)

• Compare the graph of the normal distribution of x
  (whole population) to the graph of the normal
  distribution of (means of the samples that are
  taken, that is, sample means). In your
  discussion be sure to include comparison of the
  means, standard deviations.
• Could the two curves coincide exactly?

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Writing Assignment IX (Week 11)

• Cancer patients using a certain treatment have an
  average survival time of 2 years with a standard
  deviation of 4 months. A physician claims that
  his new method of treatment increases the average
  survival time of patients, while keeping the
  standard deviation the same.
•  
• 100 randomly chosen patients who received this
  new treatment had an average survival time of 26
  months.

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• 1) What is the probability that 100 randomly
  chosen patients had an average survival of 26
  months or more?
• 2) Interpret the result of problem 1 in a
  paragraph, defending your reasoning whether the
  claim that the new treatment is more effective or
  is bogus (not more effective).

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Steps For Completing The Final Project

• (1) Use the Internet to obtain sample data. There
  are many, many possibilities here, depending
  mainly on you own interests. The only
  restriction is that the data that you choose must
  be part of a larger whole. For example, data
  collected over the 50 states on teenage pregnancy
  would be a natural sample of national teenage
  pregnancy. Data collected over various countries
  could be a reasonable sample of global data,
  but you would have to be careful about country
  selection.
• Task assigned week 1. Due date Beginning of
  week 3. Feedback week 4.

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• (2) Compute the descriptive statistics for your
  data (mean, mode, median, standard deviation,
  minimum, maximum, quartiles), and prepare a
  histogram and box plot.
• Task assigned beginning of week 4. Due date
  beginning of week 5. Feedback end of week 5.

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• (3) Describe in your own words the data you have
  chosen for your project, and why you have
  selected it. What goals do you hope to achieve
  in carrying out your project? Please include in
  this writing a discussion of any formulas you
  will use in the computation section to follow.
  Define the variables used in the formulas.
• Task assigned beginning of week 4. Due date
  beginning of week 7. Feedback beginning of week
  9.

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• (4)   Carry out the computation at a confidence
  level of 95.
• Task assigned end of week 9. Due date end of
  week 11. Feedback week 12.
•  
• (5) Write a cogent conclusion for your project
  and submit the completed work to your teacher.
• Task assigned end of week 9. Due date end of
  week 11. Feedback week 12.

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Questions ?

• Workload?
• Time?
• Class size?
• Other?

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YOU CAN FIND THIS INFORMATION IN OUR COURSE WEB
SITEhttp//faculty.lagcc.cuny.edu/rsezer/