Juddi Trent is interested in how three of the characteristics she measured for t
ID: 3221659 • Letter: J
Question
Juddi Trent is interested in how three of the characteristics she measured for the 2012 New Hampshire data correlate with one another. Given that all of these variables are measured at the interval level of measurement, the correlation can measure their relationships. Specifically, she wants to know the size, and statistical significance of, correlations among responses to three characteristics or issues: (1) It is important that the candidate is compassionate about the needs of people (Compass R); (2) It is important that the country elect a woman as president or vice president (WomanR); and (3) It is important that the candidate talk about his/her personal religious beliefs (ReligionR). Given the output below, answer the following questions (use another sheet if necessary) A. What is the correlation for each pair of variables? (There are 3 correlations in the output.) B. How many degrees of freedom (i.e., df) are there for each correlation? C. Is each correlation statistically significant? [Assume alpha =.05.] How do you know? What should you do with the null hypothesis for each significant correlation? D. If the correlation between variables is significant, what is the nature of the correlation? (In other words, is the correlation positive or negative?) Is the relationship between variables consistent with Juddi's alternative hypotheses? E. Compute the coefficient of determination for each significant correlation. Does this represent a small, medium, or large effect as discussed in class?Explanation / Answer
Answer:
A.
Correlation between CompassR and WomanR =0.203
Correlation between CompassR and ReligionR =0.056
Correlation between WomanR and ReligionR =0.116
B).
Df for Correlation between CompassR and WomanR =250
Df for Correlation between CompassR and ReligionR =252
Df for Correlation between WomanR and ReligionR =251
C).
Test for Correlation between CompassR and WomanR =0.203
Right tailed test. Calculated one tailed P=0.001/2 =0.0005 which is < 0.05 level.
Reject Ho. Correlation is significant.
Test for Correlation between CompassR and ReligionR =0.056
Left tailed test. Calculated one tailed P=0.374/2 =0.187 which is > 0.05 level.
Do not reject Ho. Correlation is not significant
Test for Correlation between WomanR and ReligionR =0.116
Two tailed test. Calculated P=0.065 which is > 0.05 level.
Do not reject Ho. Correlation is not significant.
D).
Correlation between CompassR and WomanR is positive.
Correlation between CompassR and ReligionR is positive.
Correlation between WomanR and ReligionR is positive.
E).
Coefficient of determination between CompassR and WomanR =0.203*0.203 = 0.041209
Size is small.
Coefficient of determination between CompassR and ReligionR =0.056*0.056 =0.003136
Size is small.
Coefficient of determination between WomanR and ReligionR =0.116*0.116 =0.013456
Size is small.
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