PRACTICE OF STATS - 1 TERM ACCESS CODE
PRACTICE OF STATS - 1 TERM ACCESS CODE
4th Edition
ISBN: 9781319403348
Author: BALDI
Publisher: Macmillan Higher Education
Question
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Chapter 11, Problem 11.50E

(a)

To determine

To make your own Normal quantile plot of the data in Group 3 for plots of forest that were logged 8 years earlier and first, sort and rank the data from smallest to largest, second, calculate z-scores for the adults and third, make a scatterplot of the number of trees per plot against their calculated z-scores.

(a)

Expert Solution
Check Mark

Explanation of Solution

In the question, the data is given that described of the effects of logging on counts in the Borneo rainforest as:

    Group 3
    18
    4
    22
    15
    18
    19
    22
    12
    12

Thus, firstly we will sort the data from smallest to largest by using excel. That is first we will select the data and click the sort and filter option and then select ascending order. Thus, the result will be as:

    Group 3
    4
    12
    12
    15
    18
    18
    19
    22
    22

Now we will use the R programming to construct the Normal quantile plot and scatterplot by using the codes as:

  G=c(18,4,22,15,18,19,22,12,12)z=qnorm(((1:9)0.5)/9)library(plotly)data=data.frame("No_of_trees"=G,"Normal_scores"=z)figg=plot_ly(data=data,x=~Normal_scores,y=~No_of_trees)figgplot(x=z, y=G,col="red",xlab="Normal_scores",ylab="No_of_trees",main="Normal Quantile Plot")qqnorm(data$No_of_trees,pch=1, frame=FALSE)qqline(data$No_of_trees,col="blue",lwd=2)

And the plots are as:

  PRACTICE OF STATS - 1 TERM ACCESS CODE, Chapter 11, Problem 11.50E , additional homework tip  1

The above plot is Normal quantile plot which shows the Normality of the data and in this we can see that the points are approximately in a straight line and increasing.

  PRACTICE OF STATS - 1 TERM ACCESS CODE, Chapter 11, Problem 11.50E , additional homework tip  2

This is the scatterplot of the data which shows the increasing nature of the graph and it is also in a straight line.

  PRACTICE OF STATS - 1 TERM ACCESS CODE, Chapter 11, Problem 11.50E , additional homework tip  3

(b)

To determine

To examine your Normal quantile plot for deviations from Normality and explain your conclusions.

(b)

Expert Solution
Check Mark

Explanation of Solution

In the question, the data is given that described of the effects of logging on counts in the Borneo rainforest as:

    Group 3
    18
    4
    22
    15
    18
    19
    22
    12
    12

Thus, from the scatterplot in the part (a), we can say that if Normal scores increases the number of trees will also increase. The points seem to fail about a straight line and the x-axis plots the theoretical quantiles. Those are the quantiles from the standard Normal distribution with mean zero and standard deviation one. And also all the points are very close to the line constructed in the plot and so the data shows Normality.

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