Time Wasted a Group of Students Decide to See If

question 11

Essay

Time Wasted A group of students decide to see if there is link between wasting time on the
internet and GPA. They don't expect to find an extremely strong association, but they're
hoping for at least a weak relationship. Here are the findings. $$\begin{array} { | l | l | l | } \hline \text { linear regression results: } & & \\\text { Dependent Variable: GPA } & & \\\text { Sample size: } 10 \\\text { R (correlation coefficient) } = - 0.37199274 & & \\\text { R-sq } = 0.1383786 & & \\s = 0.85365134 & & \\& & \\\text { Parameter } & \text { Estimate } & \text { Std. Err. } \\\hline \text { Intercept } & 4.06191 & 0.74405 \\\hline \text { Hours/week } & - 0.0297 & 0.02616 \\\hline & & \\\hline\end{array}$$
a. How strong is the relationship the students found? Describe in context with statistical
justification.
One student is concerned that the relationship is so weak, there may not actually be any
relationship at all. To test this concern, he runs a simulation where the 10 GPA's are
randomly matched with the 10 hours/week. After each random assignment, the correlation
is calculated. This process is repeated 100 times. Here is a histogram of the 100 correlations.
The correlation coefficient of -0.371 is indicated with a vertical line.
b. Do the results of this simulation confirm the suspicion that there may not be any
relationship? Refer specifically to the graph in your explanation.

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