Statistics Through Applications
Statistics Through Applications
2nd Edition
ISBN: 9781429219747
Author: Daren S. Starnes, David Moore, Dan Yates
Publisher: Macmillan Higher Education
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Chapter 4.1, Problem 4.13E

(a)

To determine

To construct the scatterplot of the data given in the question and by examining the scatterplot tell about the correlation.

(a)

Expert Solution
Check Mark

Explanation of Solution

The scatterplot of the data is as follows:

  Statistics Through Applications, Chapter 4.1, Problem 4.13E , additional homework tip  1

By looking at the scatterplot we can say that, since the scatterplot slopes upwards we can expect a positive relation and since the points are far apart we expect it to be to 1 .

(b)

To determine

To calculate the correlation r of the height of the men and women.

(b)

Expert Solution
Check Mark

Answer to Problem 4.13E

The correlation is r=0.5653 .

Explanation of Solution

The mean of x is:

  x¯=66+64+66+65+70+656x¯=66

Now to calculate standard deviation of x :

Consider the following table-

  Statistics Through Applications, Chapter 4.1, Problem 4.13E , additional homework tip  2

Then the sum of the numbers in the last column to get;

  (xiX¯)2=22

Calculate σ using the above formula;

  σ=(xiX¯)2n1σ=2261σ2.0976

The mean of y :

  y¯=72+68+70+68+71+656y¯=69

The standard deviation of y :

Consider the table-

  Statistics Through Applications, Chapter 4.1, Problem 4.13E , additional homework tip  3

Now we calculate the sum of numbers in the last column to get;

  (yiY¯)2=32

Calculate σ using the above formula;

  σ=(yiY¯)2n1σ=3261σ2.5298

The correlation is determined with the formula:-

  r=1n1[(xx¯sx)(yy¯sy)]

Now, we will find the value of x.y,x2,y2 as,

  x=396y=414x.y=66×72+64×68+66×70+65×68+70×71+65×65xy=27339x2=662+642+662+652+702+652x2=26158y2=722+682+702+682+712+652y2=28598

Now computing in the correlation formula we get,

  r=1n1[(xx¯sx)(yy¯sy)]r=n.xyxy[nx2(x)2].[ny2(y)2]r=6×27339396×414[6×261583962].[6×285984142]r=0.5653

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