Statistics for People Who (Think They) Hate Statistics, Salkind, Without CD
Statistics for People Who (Think They) Hate Statistics, Salkind, Without CD
5th Edition
ISBN: 9781452277714
Author: Neil J. Salkind
Publisher: SAGE Publications, Inc
Question
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Chapter 5, Problem 1TP

1.

To determine

The Pearson product-moment correlation coefficient.

1.

Expert Solution
Check Mark

Answer to Problem 1TP

The correlation coefficient between number correct (out of a possible 20) and Attitude (out of a possible 100) is 0.59.

Explanation of Solution

The given information represents the data set as follows:

Number correct (out of a possible 20)Attitude (out of a possible 100)
1794
1373
1259
1580
1693
1485
1666
1679
1877
1991

Calculation:

The formula for calculating Pearson product moment is given by;

rXYnXYXY[nX2(X)2][nY2(Y)2] (1)

  • rXY is the correlation coefficient between X and Y.
  • n is the size of the sample.
  • X is the number correct (out of a possible 20) on the X variable.
  • Y is the Attitude (out of a possible 100) on the Y variable.
Number correct (X)Attitude (Y)X2Y2XY
179428988361598
13731695329949
12591443481708
158022564001200
169325686491488
148519672251190
166625643561056
167925662411264
187732459291386
199136182811729
15679724766472712568

Substitute 156 for X, 797 for Y, 2476 for X2, 6472 for Y2, 12568 for XY and 10 for n in the above equation (1).

rXY=10×12568156×797[10×2476(156)2][10×6472(797)2]=1348[2476024336][647270635209]=1348424×12061=0.59

The correlation between number correct and attitude is positive because the value of correlation coefficient is (0.59) lies in between 0 to 1.

2.

To determine

The scatter plot for the 10 pairs of correct and attitude; whether direct or indirect correlation would be predicted or not based on the scatterplot.

2.

Expert Solution
Check Mark

Answer to Problem 1TP

There is a direct relationship between number of correct and attitude because, if the value of correct increases then the value of attitude will also increase.

Explanation of Solution

Calculation:

Take number correct on the X-axis and attitude on the Y-axis to sketch the scatter plot.

The scattered plot is obtained as:

Statistics for People Who (Think They) Hate Statistics, Salkind, Without CD, Chapter 5, Problem 1TP

Fig (1)

The above scatter plot represents the direct relationship between number of correct and attitude because, if the value of number correct increases then the value of attitude will also increase.

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