Q.4.169 - Elementary Statistics

Question

Exercise 4.149 

 Following are the data on study time and score for calculus students from Exercises $4.63$ and $4.103$.

a. construct a scatterplot for the data.

b. decide whether using the rank correlation coefficient is reasonable.

c. decide whether using the linear correlation coefficient is reasonable.

d. find and interpret the rank correlation coefficient.

Step-by-Step Solution

Answer

(a)

(b)The rank correlation is reasonable.

(c) Linear correlation coefficient reasonable.

(d)The rank correlation coefficient has a value of $-0.928$. It shows that the variables rank time and rank score have a strong negative linear connection.

Part (a)Step 1: Given information

Given in the question that, From exercise 4.149

Following are the data on study time and score for calculus students from Exercises $4.63$ and $4.103$.

We need to  construct a scatterplot for the data .

Part(a) Step 2: Explanation

Given data is,

$\begin{array}{|lllllllll|}\hline X& 10& 15& 12& 20& 8& 16& 14& 22\\ Y& 92& 81& 84& 74& 85& 80& 84& 80\\ \hline\end{array}$

Using MINITAB, create a scatterplot for the supplied data.

Procedure for MINITAB:

Step 1: Select Scatterplot $>$ Graph.

Step 2: Click OK after selecting With Connect Line.

Step 3: Add a column of Volume to the $Y$ variables.

Step 4: Create a Diameter column under $X$ variables.

Step 5: Click the OK button.

OUTPUT FROM MINITAB:

It is clear from the graph that time and score have a negative linear connection.

Part(b) Step 1: Given information

Given in the question that, From exercise 4.149

Following are the data on study time and score for calculus students from Exercises 4.63 and 4.103.

We need to decide that  whether the use of  rank correlation coefficient is reasonable. 

Part (b) Step 2: Explanation

The given data is

$\begin{array}{|lllllllll|}\hline X& 10& 15& 12& 20& 8& 16& 14& 22\\ Y& 92& 81& 84& 74& 85& 80& 84& 80\\ \hline\end{array}$

Determine whether or not applying the rank correlation coefficient is appropriate.

Because the variable time grows as the variable score drops, the rank correlation coefficient is fair. That is, the smaller time values are associated to the larger score values, and the larger time values are related to the larger score values.

Part(c) Step 1: Given information

Given in the question that, From exercise 4.149

Following are the data on study time and score for calculus students from Exercises 4.63 and 4.103.

We need to decide that  whether the use of  linear correlation coefficient is reasonable. 

Part(c) Step 2: Explanation

Determine whether or not applying the linear correlation coefficient is appropriate.

The linear correlation coefficient is appropriate since the data appears to follow a linear trend.

Part(d) Step 1: Given information

Given in the question that, From exercise 4.149

Following are the data on study time and score for calculus students from Exercises 4.63 and 4.103.

We need to find and interpret the rank correlation coefficient. 

Part(d) Step 2: Explanation

MINITAB can be used to calculate the rank correlation coefficient.

To begin, use the MINITAB technique to get the rank for diameter and volume:

First, go to Data >Rank.

Step 2: Select Time in Rank data in.

Step 3: Select Rank Time from the Store Ranks in menu.

Step 4: Select Score in Rank data.

Step 5: Select Rank Score from the Store Ranks menu.

Correlation:

Procedure for MINITAB:

Step 1:Select Stat >Basic Statistics >Correlation in the first step.

Step 2: Select Rank Time and Rank Score from the left-hand box in Variables.

Step 3: Press the OK button.

MINITAB output: Rank Time, Rank Score correlation

Pearson correlation of Rank Time and Rank Score $=-0.928$

$P-\text{ Value }=0.001$

$=-0.928$ 

The rank correlation coefficient obtained from MINITAB is $-0.0928$.

Interpretation: The rank correlation coefficient has a value of $-0.928$. It shows that the variables rank time and rank score have a strong negative linear connection.