A Counselor Working with Teenagers Is Interested in the Relationship

question 14

Essay

A counselor working with teenagers is interested in the relationship between anxiety and depression.The counselor administers a depression and anxiety test to each teenager.The scores obtained from the administration of the two inventories are given below. $$\begin{array} { | | c | c | | } \hline \hline \text { Anxiety } & \text { Depression } \\\hline 22 & 16 \\\hline 12 & 8 \\\hline 68 & 33 \\\hline 10 & 6 \\\hline 5 & 5 \\\hline 53 & 24 \\\hline 44 & 18 \\\hline 37 & 17 \\\hline 0 & 2 \\\hline 21 & 14 \\\hline 64 & 31 \\\hline 33 & 17 \\\hline 55 & 30 \\\hline 18 & 13 \\\hline 3 & 3 \\\hline 4 & 4 \\\hline 11 & 7 \\\hline 13 & 9 \\\hline 7 & 5 \\\hline \hline\end{array}$$
$\begin{array}{llr}\text { The summary statistics are }&\text { Anxiety }&\text { Depression }\\\text { Sample mean } & 25.2632 & 13.7895 \\\text { Standard deviation } & 21.9895 & 9.8464\end{array}$

$\sum_{i=1}^{19}\left(x_{1}-\bar{x}\right)\left(y_{i}-\bar{y}\right)=3828.0526$
a.What do these data say about the level of anxiety and depression in these teenagers?
b.What is the correlation between anxiety and depression? What does this number tell you?
c.What is the correlation coefficient between anxiety and depression? What does this number tell you?
d.If you were counseling a teenager with high levels of anxiety,what would you expect their level of depression to be?

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Definitions:

Compensating Differentials

Wage differentials that arise from the need to compensate workers for non-monetary aspects of a job, such as difficult working conditions or undesirable locations.

Midnight Shift

A work schedule that typically runs through the night hours, often starting at or around midnight and lasting until morning.

Efficiency Wages

A theory in labor economics that suggests higher wages can increase worker productivity and efficiency, often leading to lower turnover and improved quality of work.

Prevailing Wage

The average wage paid to similarly employed workers in a specific region, occupation, or industry.