STAT100 Assignment 3: Chapters 10, 11 & 13 [Total: 25 marks]
Assignment 3: Chapters 10, 11 & 13
[Total: 25 marks]
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 botanists 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.)
(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.
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