5. For the data presented below, answer the questions that follow.

Score on political Score on current
Individual awareness test events test
1 24 23
2 16 12
3 11 11
4 9 6
5 8 13
6 14 11
7 17 16
8 19 16
9 21 21
10 25 25
11 18 11
12 13 13
13 11 14
14 6 10
15 9 10
16 12 7
a. Construct a scatterplot.
b. Draw a regression line through the data point that “fits” the data points reasonably well.
c. Enclose the data points with a ellipse.
d. Estimate the direction of the correlation.
e. Estimate the strength of the correlation coefficient.
f. Now, use only the data points associated with current event scores of 15 and lower and indicate the effects this has on the direction and strength of the correlation coefficient.
g. Explain why this is the case.
h. Explain in words what a non-truncated scatterplot means.
i. Identify how likely it is that a causal relationship has been indicated.

a. To construct a scatterplot, we will plot the data points on a graph where the x-axis represents the score on the political awareness test and the y-axis represents the score on the current events test.

Here is the scatterplot:

```
| x
25 | x
| x
| x
20 |
| x x
| x x
15 | x
| x
| x
10 |
| x x
| x
5 |
|
|
0 +-------------------------
0 5 10 15 20 25
Political Awareness Test Score
```

b. Drawing a regression line through the data points that "fits" the points reasonably well, we get:

```
| x
25 | x
| x
| x
20 | ------ x
| x | | x
| x x
15 | ---- x
| x
| x
10 | x
| x x
| x
5 |
|
|
0 +-------------------------
0 5 10 15 20 25
Political Awareness Test Score
```

c. Enclosing the data points with an ellipse, we get:

```
| x
25 | x
| x
| x
20 | ------ x
| x | | x
| x x
15 | |------|
| | |
| -----
10 | x
| x
| x
5 |
| x
|
0 +-------------------------
0 5 10 15 20 25
Political Awareness Test Score
```

d. From the scatterplot, we can estimate that there is a positive correlation between the two variables. As the score on the political awareness test increases, so does the score on the current events test.

e. The strength of the correlation coefficient can be estimated visually from the scatterplot. In this case, the correlation appears to be moderately strong.

f. If we use only the data points associated with current event scores of 15 and lower, it means we are limiting the range of scores considered in the analysis. This may affect the direction and strength of the correlation coefficient.

g. This is the case because by limiting the range of scores, we may not have a representative sample of the relationship between the two variables. It is possible that the correlation appears weaker or even changes direction when considering only a restricted range of scores.

h. A non-truncated scatterplot refers to a plot that includes all the data points and does not exclude any values based on specific criteria.

i. Based on the information provided, we cannot determine if a causal relationship has been indicated. A correlation does not imply causation. Other factors and variables not measured in this data set may be responsible for the observed relationship.

To analyze the given data and answer the questions, you will need to follow these steps:

a. Construct a scatterplot:
A scatterplot is a graph that displays the relationship between two variables. In this case, the variables are the score on the political awareness test and the score on the current events test. Plot each data point on the graph, with one variable on the x-axis and the other on the y-axis.

b. Draw a regression line:
A regression line shows the general trend or pattern of the data. Draw a line that appears to fit the data points reasonably well. The line should follow the general direction of the data points.

c. Enclose the data points with an ellipse:
An ellipse encloses the data points and helps visualize the spread or distribution of the data. Draw an ellipse to include most of the data points.

d. Estimate the direction of the correlation:
Examine the scatterplot and the regression line. Determine if the data points generally slope upwards (positive correlation), downwards (negative correlation), or have no specific pattern (no correlation).

e. Estimate the strength of the correlation coefficient:
The strength of the correlation can be assessed by looking at how closely the data points cluster around the regression line. If the data points are tightly packed around the line, the correlation is strong. If they are spread out, the correlation is weak.

f. Effects of using only data points associated with current event scores of 15 and lower:
Take note of the scores on the current events test, and select only the data points that have a score of 15 or lower. Plot these selected points on a separate scatterplot.

g. Explanation for the effects on direction and strength:
Based on the new scatterplot, compare the direction and strength of the correlation with the original scatterplot. Assess if the direction and strength have changed and explain why this might be the case.

h. Non-truncated scatterplot:
A non-truncated scatterplot includes all the available data points and provides a comprehensive visual representation of the relationship between the variables. It does not exclude any data points based on specific criteria.

i. Likelihood of a causal relationship:
To determine the likelihood of a causal relationship, you need additional evidence beyond correlation. Correlation only indicates a relationship between variables, but does not necessarily imply causation. To establish causation, you would need to conduct further research and gather additional evidence.