Chapter 7, Problem 34E

(a)

To determine

To create a scatterplot.

Explanation of Solution

A survey was conducted in United States and ten countries of Western Europe to determine the percentage of teenagers who had used marijuana and other drugs. The scatterplot for the marijuana and the other drugs is as follows:

  

On the horizontal axis there is Marijuana and on the vertical axis there is Other drugs.

(b)

To determine

To calculate what is the correlation between the percent of teens who have used marijuana and the percent who have used other drugs.

Answer to Problem 34E

The correlation between the marijuana and the other drugs is $0.9341$ .

Explanation of Solution

A survey was conducted in United States and ten countries of Western Europe to determine the percentage of teenagers who had used marijuana and other drugs.

Then we will calculate the correlation coefficient of marijuana and the other drugs by using the excel. The data is as:

Marijuana	Other Drugs
22	4
17	3
40	21
5	1
37	16
19	8
23	14
6	3
7	3
53	31
34	24

Formula used:

The CORREL function calculates the correlation coefficient between the two data sets in the excel. The syntax is as:

CORREL(array $1$ ,array $2$ )

Calculation:

Now, we will calculate the correlation coefficient using the excel. We will use the above CORREL function for this and we will have,

  $=\text{CORREL}\left(\text{G8:G22,H8:H22}\right)$

And the answer to this will be as:

Correlation coefficient

0.9341

So, the correlation between the marijuana and the other drugsis $0.9341$ .

(c)

To determine

To write a brief description of the association.

Explanation of Solution

A survey was conducted in United States and ten countries of Western Europe to determine the percentage of teenagers who had used marijuana and other drugs. And the correlation between the marijuana and the other drugs is $0.9341$ .

Now, we have since the scatterplot has points in an upward direction it seems that the greater the percent of marijuana users, the greater the percent of the other drugs users. As we can see that the relationship is positive and the dots in the scatterplot are moving upwards. And also there is strong relationship between the marijuana and the other drugs as the correlation coefficient is closer to one.

(d)

To determine

To explain do these results confirms that marijuana is a “gateway drug”, that is, that marijuana use leads to the use of other drugs or not.

Answer to Problem 34E

Yes.

Explanation of Solution

A survey was conducted in United States and ten countries of Western Europe to determine the percentage of teenagers who had used marijuana and other drugs.And the correlation between the marijuana and the other drugs is $0.9341$ .

Yes, these results confirms that marijuana is a “gateway drug”, that is, that marijuana use leads to the use of other drugsbecause there is a strong correlation between Marijuana and other drugs as there correlation coefficient is closer to one.