Please help Correlation sheet

Fill in the blanks:

 

8.1.      The magnitude of the correlation is indicated by the correlation _____ which can range from -1.00 to +1.00.

 

8.2.      The most common and efficient way to present the correlations of several variables with each other is by using a(n) ______ table.

 

8.3.      The correlation between two variables can be shown graphically by a ________.

 

8.4.          The null hypothesis predicts that the correlation coefficient is equal to _______.

 

8.5.           The Spearman rank order correlation is used when the variables to be correlated are measured on a(n)  ______ scale.

 

 

Circle the correct answer:

 

8.6.      The hypothesis that states that r¹0 is an example of a(n) alternative/null hypothesis.

 

8.7.      When an increase in one variable is associated with a decrease in the other variable, the correlation between these two variables is positive/negative.

 

8.8.      In order to use the Pearson product-moment correlation, the variables to be correlated should be measured on an ordinal/interval scale.

 

8.9.      When the points on a scattergram go from the bottom left to the top right they represent a positive/negative correlation.

 

8.10.       The true correlation between two variables may be underestimated when the variance of one of the variables is very high/very low.

 

8.11.       When the null hypothesis is rejected at p<.001, it means that the chance that r=0 is very small/very high.

 

8.12.       The null hypothesis is rejected when the obtained correlation coefficient is higher/lower than the critical value.

 

 

Answer/compute the following questions:

 

8.13     Which correlation coefficient (a or b) shows a stronger relationship between the two variables being correlated?

 

a.         X1&Y1: r =  .85

 

b.         X2&Y2: r = -.94

 

8.14.    Following are two scattergrams (in Figure A and in Figure B). Four different correlation coefficients are listed under each scattergram. Choose the coefficient that best matches each scattergram.

 

         Y                                                                       Y

        

                                 ·                                                                            ·  ·

                ·            ·                                                                              Â·  ·   

                        ·                 ·                                                                ·    · 

                       ·             ·                                                                  Â·    ·   

                         ·                ·                                                          Â·  ·    ·

                   ·                                                                                Â·   ·   · 

                           ·               ·                                                       Â·  ·

                   ·                ·                                                             ·    ·             

                         ·                ·                                                    ·    ·  

                              ·                                                           Â·    ·

                                                      X                                                                           X

 

                        Figure A                                                         Figure B

 

                        A1. r= .50                                                      B1. r= -.57

                        A2. r= .78                                                      B2. r=   .92

                        A3. r= -.10                                                      B3. r=   .38

                        A4. r= -.89                                                      B4. r=  -.91

 


8.15     Following is a scattergram showing the scores of 8 statistics students on two tests, X and Y. Each of the first 7 students is represented by a dot and their scores are listed in the table that follows. Use the scattergram to find the scores of student #8 on test X and test Y. The location of this student on the scattergram is represented by a large dot (•) next to number 8.

 

           

               Y

                                         1                             4

4                           ·                              ·

 

                                         5          2    

            3                           ·          ·

 

                                         6          8

            2                           ·          ·

           

                             7          3

            1               ·          ·

                                                                                    X

                             1          2        3        4        5

 

                                                                       

Student #       X         Y

 

        1              2          4

        2              3          3

        3              2          1

        4              5          4

        5              2          3

        6              2          2

        7              1          1

 

        8              ?          ?

 

 

 


8.16     What do these two scattergrams have in common?

           

           Y                                                              Y

       
   

 

 

                ·   ·    ·  ··    ·   ··   ·    ·

                  ·   ·    ·  ··    ·   ··   ·     ·

               ·   ·    ·  ··    ·   ··   ·    ·  ··                                    ·   ·    ·  ·  ·  ·  ··  ····  · 

               ·   ·    ·  ··    ·   ··   ·    ·  ··  

                 ·   ·    ·  ··    ·   ··   ·    ·

    ·   ·    ·  ··    ·   ··   ·    ·  ··          

                 Â·    ·  ··    ·   ··   ·    ·  ··  

           

 

8.17     Estimate (do not calculate!) the correlation between the advertising spending and sales that were obtained over a 5 year span. Indicate whether the correlation is positive or negative, and whether it is high or low. Explain your answer.

 

                Year                        Ad Spending              Sales

 

       1                               $21,000                   $83

       2                                 15,000                      70

       3                                 17,000                      68

       4                                 25,000                      90

       5                                 19,000                      74

 

8.18     Estimate (do not calculate!) which of the two sets of consumer research studies (A&B or X&Y) has a higher correlation. Explain your answer.

 

                        Set 1                                                               Set 2

           

            Study #           A         B                                 Study #    &nb

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