# STAT100 Assignment 3 Chapters 10 11 and 13

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

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STAT100

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Assignment &nbsp;3: &nbsp;Chapters 10, &nbsp;11 & 13

[Total: 25 &nbsp;marks]

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Note:

 Please refer to the relevant examples in the Study Guide, and the relevant exercises given in the Tutorial and Practical &nbsp;Exercises Workbook.

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

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

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 Explain&nbsp; your answers, and use correct &nbsp;probability notation &nbsp;where relevant.

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 Outline &nbsp;the 5 steps of hypothesis testing &nbsp;where relevant.

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 Marks are awarded &nbsp;for presentation &nbsp;and handwritten assignments &nbsp;will not be marked.

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

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

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

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(b) &nbsp;What conclusion can you draw about &nbsp;the botanists &nbsp;claim?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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