Question

In: Statistics and Probability

A psychologist would like to determine whether there is any consistent relationship between intelligence and creativity.  The...

A psychologist would like to determine whether there is any consistent relationship between intelligence and creativity.  The psychologist obtains a random sample of n = 18 people and administers a standardized IQ test and a creativity test to each individual.  Using these data, the psychologist obtains a Pearson correlation of r = +.20 between IQ and creativity.

a.  Do the sample data provide sufficient evidence to conclude that a real (non-zero)

     correlation exists in the population?  Test at the .05 level of significance.

b.  If the same correlation of r = +.20 was obtained for a sample of n = 102 people, what

     decision would you make about the population correlation?

Researchers who measure reaction time for human subjects often observe a relationship between the reaction time scores and the number of errors that the subjects commit.  This relationship is known as the “speed-accuracy trade-off.”  The following are data from a reaction time study where the researcher recorded the average reaction time (milliseconds) and the total number of errors for each individual in a sample of n =8 subjects.

Subject          Reaction Time         Errors  

    A                       184                      10
    B                       213                        6
    C                       234                        2
    D                       197                        7
    E                       189                       13
    F                       221                       10
    G                      237                         4
    H                      192                         9

a.  Compute the Pearson correlation for the data.

b.  In words, describe the speed-accuracy trade-off.

Many researchers have found a negative relationship between children’s IQ and the size of the family in which the children live.  The following hypothetical data represent 8 families.

Number of Children (X)              Children’s Average IQ (Y)

               4                                                     104

               2                                                     111

               2                                                     101

               1                                                     131

               3                                                     103

               5                                                       96

               1                                                     123

               2                                                     115

a.  Compute the Pearson correlation between family size and average IQ.

b.  Find the regression equation for using the number of children to predict the average

     IQ.

c.  What would the regression equation predict the average IQ score would be for a

     family with 10 kids?

Solutions

Expert Solution

t table as follows:

orchestra answered 1 year ago
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