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Category > Accounting Posted 28 Apr 2017 My Price 10.00

Sample correlation coefficient

 

For each of the following examples, explain whether or not it is reasonable to treat the sample correlation coefficient, r, as an estimate of a population correlation coefficient . Briefly justify your answer.

(a) The blood chemistry data from Exercise 12.2.3.

(b) The CA1 neuron data from Exercise 12.2.4.

(c) The cob weight data from Exercise 12.2.5.

(d) The fungus growth data from Exercise 12.2.6.

(e) The basal Ca pump activity from Exercise 12.2.8.

Exercise 12.2.3:

In a study of natural variation in blood chemistry, blood specimens were obtained from 284 healthy people. The concentrations of urea and of uric acid were measured for each specimen, and the correlation between these two concentrations was found to be r = 0.2291  Test the hypothesis that the population correlation coefficient is zero against the alternative that it is positive6. Let ∝ = 0.05

 

Exercise 12.2.4:

Researchers measured the number of neurons in the CA1 region of the hippocampus in the brains of eight persons who had died of causes unrelated to brain function. They found that these data were negatively correlated with age.The sample value of r was -0.63.7

(a) Is this correlation coefficient significantly different from zero? Conduct a test using ∝ = 0.10

(b) Suppose in part (a) you found that the correlation does significantly differ from zero. Does this provide

evidence that aging is a cause for CA1 neuron loss? If not, what could be said? Briefly explain.

 

Exercise 12.2.5:

Twenty plots, each  meters, were randomly chosen in a large field of corn. For each plot, the plant density (number of plants in the plot) and the mean cob weight (gm of grain per cob) were observed. The results are given in the table.8

Preliminary calculations yield the following results:

(a) Is there significant evidence for a linear relationship between cob weight and plant density? Carry out an

appropriate test using ∝ = 0.05.

(b) Is this study an observational study or an experiment?

(c) Farmers are interested in whether manipulating plant density can alter cob weight. Could these data

be used to answer this question? If not, what could be said? Briefly explain.

 

Exercise 12.2.6:

6Laetisaric acid is a compound that holds promise for control of fungus diseases in crop plants. The accompanying data show the results of growing the fungus Pythium ultimum in various concentrations of laetisaric acid. Each growth value is the average of four radial measurements of a P. ultimum colony grown in a petri dish for 24 hours; there were two petri dishes at each concentration.9

(a) Is there significant evidence for a linear relationship between fungus growth and acid concentration?

Carry out an appropriate test using ∝ = 0.05.

(b) Is this study an observational study or an experiment?

(c) It is suggested that acid could be used to retard fungus growth. Could these data be used to verify

this claim? If not, what could be said? Briefly explain.

Exercise 12.2.8:

Cellular ability to regulate homeostasis is measured by basal Ca pump activity. Deregulation of calcium

homeostasis can trigger serious effects of cell functioning. Can maternal mercury exposure measured by mercury deposits in hair (_g/g) affect newborn’s basal Ca pump activity (nmol/mg/hr)? The following data summaries and graph are from a human study involving a sample of 75 newborns and their mothers.11

(a) It is a good habit to always plot our data before analysis. Examining the preceding scatterplot, does

there seem to be a linear trend in the data? Is it increasing or decreasing? Is it weak or strong?

(b) Examining the plot, we see there is a mother with a maternal hair level around 4.2 _g/g. If her child’s

basal Ca pump activity were changed from about 2800 to about 2000 nmol/mg/hr, would the sample

correlation increase or decrease?

(c) Is there evidence that newborn basal Ca pump activity linearly decreases with maternal hair level? Carry

out an appropriate test using ∝ = 0.05.

(d) In part (c) you should have found that there is strongevidence for a linearly decreasing relationship between

X and Y. Explain how the evidence can be so strong even though the graph displays substantial scatter and the sample correlation is not close to .

(e) Based on your answer to part (c) and the design of this study, what can we say regarding the primary

research question: Is there statistical evidence that maternal mercury exposure measured by mercury

deposits in hair (μg/g) affects newborn’s basal Ca pump activity (nmol/mg/hr)? -1

 

 

 
 

Answers

Alpha Geek
(8)
Status NEW Posted 28 Apr 2017 09:04 AM My Price 10.00

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