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Name_________________________________________________________________

In these problems, you will:

• Interpret the values of Pearson’s correlation coefficient

• Describe what correlation means

• Calculate Pearson’s correlation coefficient by hand and in excel

• Interpret excel output for Pearson’s correlation coefficient

Please answer the following on this page or on additional paper if needed. You must show all of your work to receive full credit for your answers.

• For any math problem, your final answer must be enclosed in a box.

• Your homework must be completed independently, or it is considered academic dishonesty

• For any excel problem., you must submit your excel workbook with your problem set as instructed

1. Interpret the following Pearson correlation coefficients:

1. An r of .23 between the number of hours spent with friends after school and self reported delinquency.

1. An r of .-78 between hours money spent on welfare and crime rates.

2. According to your reading from Naked Statistics, correlation does not mean that one variable causes the values of the other variable. Provide an example not in the reading of two variables that are likely correlated but not causally related. Explain why one variable’s values does not cause the other variable’s values.

3. If you have a calculated value of r that equals .727 and N=10, are you able to reject a null hypothesis tested at the .01 level of significance? Indicate with specifics as to how you can tell.

4. According to your reading from Naked Statistics, the correlation coefficient has “no units attached to it”. Explain what is meant by this statement, and why it is beneficial.

5. In their 1993 research, Grasmick and colleagues studied the relationship between low self-control and self-reported criminal activity. You decide to replicate the study. You take a sample of 10 people and measure their levels of self-control (using a 23-item scale that creates an interval-level variable) and number of self-reported acts of delinquency. Using the data below, create a null and research hypothesis and calculate the value of r and test for its significance with an alpha of .01. Provide a conclusion about the strength and direction of correlation as well as a conclusion regarding your hypothesis test.

Table of Data from 10 People on Their Self-Control and Delinquency

6. Use the data above in excel to test your null hypothesis. You must enter these data yourself into a blank excel workbook. You must save your excel workbook as “Problem Set 8 Workbook” and include on the first worksheet these data and your excel output. Highlight in yellow the value of the correlation coefficient in your worksheet. Perform correlation in excel. Provide a conclusion about the strength and direction of correlation as well as a conclusion regarding your hypothesis test. Provide detail as to how you know whether you can reject your null hypothesis.