STAT100 Assignment 3: Chapters 10, 11 & 13 [Total: 25 marks]

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STAT100

 

Assignment  3:  Chapters 10,  11 & 13

[Total: 25  marks]

 

Note:

• Please refer to the relevant examples in the Study Guide, and the relevant exercises given in the Tutorial and Practical  Exercises Workbook.

 

• Refer to Assignment presentation guidelines, and the sample assignment.

 

• Unless indicated  otherwise, use Rcmdr for your calculations/ analyses.  Include relevant Rcmdr output with your solutions.  Use courier font when inserting output in your assign- ment.  This will automatically align columns etc.

 

• Explain  your answers, and use correct  probability notation  where relevant.

 

• Outline  the 5 steps of hypothesis testing  where relevant.

 

• Marks are awarded  for presentation  and handwritten assignments  will not be marked.

 

Question 1 (Chapter 10)                                                                                                       [6 marks] A botanist  has produced a new variety of hybrid wheat that  is better  able to withstand drought. The botanist  knows that  for the parent plants 80% of seeds germinate.  The botanist  also claims that  the proportion of seeds germinating for the new hybrid  plant is also 80%.

Four  hundred  seeds from the hybrid  plant are tested  and 308 seeds germinate.

 

(a)  Calculate  a 95% confidence interval for the true  proportion of seeds that  germinate  from the new hybrid.

 

(b)  What conclusion can you draw about  the botanist’s  claim?

 

Source: C. H. Brase & C. P. Brase Understanding Basic  statistics (5ed)  (2010), Brooks/Cole, p.  386.

 

Question 2 (Chapters 11  & 13)                                                                                        [12 marks] The amount of sewage and industrial  pollutants  dumped into a body of water affects the health of the water  by reducing the amount of dissolved oxygen available for aquatic  life.

Fifteen samples were taken from a river at a location one kilometre downstream  and also from a location  one  kilometre  upstream  from a sewerage plant.   The  data  are stored  in oxy.txt.

Source: R. L. Ott  & M. Longnecker Statistical  Methods & Data  Analysis  (5ed) (2001), Duxbury,  pp.  280-281.

 

(a)  Current  research asserts  that  the mean dissolved oxygen level must  be at  least 5 parts per million for fish to survive.

(i) Using Rcmdr calculate  the mean and sd of the downstream  data.

(ii) Showing all calculations, find a 95% confidence interval for the mean oxygen content downstream  from the plant.  (Do not use Rcmdr.)

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(iii) Does the mean oxygen level appear to be sufficient to support  fish life? Justify  your response.

(b)  Do the  data  provide sufficient evidence to indicate  a difference in mean  oxygen content between  locations  upstream   and  downstream  from the  sewerage plant?        Conduct  the appropriate test of hypothesis, justifying your conclusion.

 

Question 3 (Chapters 6 & 13)                                                                                            [7 marks] A randomized,  double-blind experiment studied  whether magnetic fields applied over a painful area can reduce pain intensity.  The subjects were 50 volunteers with post polio syndrome, who reported  muscular  or arthritic pain.  The pain level was graded  subjectively on a scale from 0 (no pain)  to 10 (maximum pain).  Patients were randomly  assigned to wear either  a magnetic device or a placebo device over the painful area for 45 minutes.

 

(a)  With reference to the context of this problem explain what is meant by the term “double- blind ” and why it is an important part  of the design of this experiment.

 

(b)  All patients rated their pain before and after application  of the device. For the 29 patients assigned to the  magnetic  group,  the mean pain scores before and after  treatment were

9.6 and 4.4 respectively.  Explain  briefly why a matched  pairs procedure should be used to assess whether application  of the magnetic device significantly lowers pain.

 

(c) The  21 patients  assigned to the  placebo device had  mean pain scores before and  after treatment of 9.5  and  8.4, respectively.  Explain  briefly why a matched  pairs  procedure should not be used to test the hypothesis that  the magnetic device is significantly better  than  the placebo at reducing pain intensity.

Source: B. Baldi & D.S. Moore (2009) The Practice  of Statistics in the Life Sciences, Freeman  p.  444.
Cartoon  Source :

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