The following data set was collected by Campus Life. They are investigating the possibility of a relationship between students' satisfaction with Penn State (on a scale of 1-10 where higher numbers indicate greater satisfaction) and how many activities they participate in on campus. In this table, each "ID" represents a single student.1. Imagine that someone in campus life wants to convert the "Satisfaction" scale of 1-10 to a scale of 1-100. 2. Would the covariance get larger, smaller, or stay the same? 3. Would the correlation coefficient r become larger, smaller, or stay the same?4. What would be an example of an impossible correlation coefficient? In other words, give a value of r that would lead you to suspect that the researcher made a mistake.5. Imagine a study where all our data (x, y) falls perfectly on a flat and straight horizontal line. If we calculated the correlation coefficient r for this data, what would it be? What would that mean for our hypotheses?Student IDSatisfactionActivities1710264320441351767157610861293810821Mean5.010.0Std.Dev2.45.9

Question

The following data set was collected by Campus Life. They are investigating the possibility of a relationship between students&#039; satisfaction with Penn State (on a scale of 1-10 where higher numbers indicate greater satisfaction) and how many activities they participate in on campus. In this table, each &quot;ID&quot; represents a single student.1. Imagine that someone in campus life wants to convert the &quot;Satisfaction&quot; scale of 1-10 to a scale of 1-100. 2. Would the covariance get larger, smaller, or stay the same? 3. Would the correlation coefficient r become larger, smaller, or stay the same?4. What would be an example of an impossible correlation coefficient? In other words, give a value of r that would lead you to suspect that the researcher made a mistake.5. Imagine a study where all our data (x, y) falls perfectly on a flat and straight horizontal line. If we calculated the correlation coefficient r for this data, what would it be? What would that mean for our hypotheses?Student IDSatisfactionActivities1710264320441351767157610861293810821Mean5.010.0Std.Dev2.45.9

Royce Moore · Accepted Answer

Step 1  In that case, on a scale of 1−100, the table and its corresponding values are;  IDX1=Satis(1−10)X2=Satis(1−100)Y=ActivityX1−m1X2−m2Y−m3(X1−m1)(Y−m3)(X2−m2)(Y−m3)17701022000026604110−6−6−6032200−3−30−1030300444013−1−103−3−3051107−4−40−312120677015220510100766010110000866012110222093308−2−20−244010880213301133330Mean5501082820  Thus, Cov(X1,Y)=8.2 and Cov(X2,Y)=82.  Thus, with increase in the satisfaction level, the covariance increases.  Step 3  b. The correlation is r1=CovX1,YsX1.sY,   or r2=CovX2,YsX2.sY  Calculating, we see that,   r1=0.661=r2.  Thus, the correlation coefficient for both the scales are same.   c. If the correlation coefficient is 0, between the two variables, then this is an impossible case and the researcher must have made a mistake, as there must be some relationship between two variables which can practically be compared. The relationship may be very small, but can never be zero.

The following data set was collected by Campus Life. They are investig

Answered question

Answer & Explanation

New Questions in High school statistics