For the following assignment, use the Rank Correlation that was demonstrated in Chapter 12 of the textbook (page 566).
Do different treatments affect the weights of poplar trees?
The Chapter Problem for Chapter 11 included the same data listed in Table 12-1, which lists weights (in kilo¬grams) of poplar trees given different treatments at differ¬ent sites. These data, taken from Data Set 9 in Appendix B, are the weights given for year 1 at Site 1, which has rich and moist soil and is located near a creek. In Chapter 11 we noted that the methods of analysis of variance require that the samples come from populations having distribu¬tions that are approximately normal. We also noted that the second sample (trees treated with fertilizer) included a weight of 1.34 kg, which appears to be an outlier. In Exer¬cise 1 from Section 11-2, the ANOVA results are shown for the data with the outlier of 1.34 kg excluded, and we can see that the results do not change dramatically. When the outlier is excluded, the F test statistic changes from 5.73 to 8.45, and the P-value changes from 0.007 to 0.002.
But what if there are more outliers, or analysis of the sam-ples strongly suggests that the samples come from popula-tions having distributions that are very far from normal? The methods of analysis of variance presented in Chap¬ter 11 could not be used with such a violation of a require¬ment that the distributions are approximately normal. In this chapter we introduce alternative methods that do not require that populations have distributions that are normal (or any other particular distribution). We will apply one of those methods to the sample weights in Table 12-1, and we will determine whether the different treatments appear to have an effect on the tree weights.
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Table 12-1
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Weights (kg) of Poplar Trees
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Treatment
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Fertilizer and
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None
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Fertilizer
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Irrigation
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Irrigation
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0.15
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1.34
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0.23
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2.03
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0.02
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0.14
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0.04
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0.27
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0.16
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0.02
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0.34
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0.92
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0.37
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0.08
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0.16
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1.07
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0.22
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0.08
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0.05
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2.38
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n
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5
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5
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5
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5 |
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x¯
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0.184
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0.332
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0.164
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1.334
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s
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0.127
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0.565
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0.126
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0.859
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Utilizing Excel or SPSS: Use a rank correlation coefficient to test for a correlation between two variables.
Rank Correlation Table
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x (cigarettes per day)
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60
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10
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4
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15
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10
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1
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20
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8
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7
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10
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10
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20
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y(cotinine)
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179
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283
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75.6
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174
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209
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9.51
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350
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1.85
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43.4
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25.1
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408
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344
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Use a significance level of σ = 0.05. The new health care program in the United States makes provisions for capitation programs where health care insurers work with clinical facilities to perform risk analysis of patients to determine the cost of providing care.
The following assignment might be used to assess how much a person smokes. When nicotine is absorbed by the body, cotinine is produced. A measurement of cotinine in the body is therefore a good indicator of how much a person smokes.
The reported number of cigarettes smoked per day and the measured amounts of cotinine (in ng/ml) are provided. (The values are from randomly selected subjects in a National Health Examination Survey.)
Is there a significant linear correlation?
How would you measure the cotinine level in the body? Explain the result.
Refer to the "Rank Correlation Table." APA format is not required, but solid academic writing is expected.
Attachment:- Problem.rar