Chapter 27, Problem 2E

a)

To determine

To explain the about the regression.

Explanation of Solution

Given:

  

The regression equation is,

  $OtherDrugs(\%)=-3.06780+0.615003(Marijuana(\%))$

On average, the other drugs use is -3.06780% when the Marijuana use is 0%. The other drugs use increases on average by 0.615003 per percent of Marijuana use.

b)

To determine

To state the hypotheses about the slope.

Answer to Problem 2E

  $\begin{array}{l}{H}_0:{\beta }_1=0\\ H_a:{\beta }_1\ne 0\end{array}$

Explanation of Solution

Given:

  

The null and alternative hypotheses:

  $\begin{array}{l}{H}_0:{\beta }_1=0\\ H_a:{\beta }_1\ne 0\end{array}$

c)

To determine

To perform the hypothesis test.

Answer to Problem 2E

There is sufficient evidence that the percentage of Other drug use change as the percentage of Marijuana change.

Explanation of Solution

Given:

  

Formula:

Test statistic:

  $t=\frac{b-{\beta }_0}{S{E}_b}$

The null and alternative hypotheses:

  $\begin{array}{l}{H}_0:{\beta }_1=0\\ H_a:{\beta }_1\ne 0\end{array}$

Test statistic:

  $t=\frac{0.615003}{0.0784}=7.8444$

The degrees of freedom = df = 9

Therefore, p-value would be,

P-value = 0 …Using excel formula, =TDIST(7.8444,9,2)

Decision: P-value < 0.05, reject H₀.

Conclusion: There is sufficient evidence that the percentage of Other drug use change as the percentage of Marijuana change.

d)

To determine

To explain R-square.

Answer to Problem 2E

87.3% of the variation between the percentage of Other drugs use and percentage of Marijuana has been explained by the regression model.

Explanation of Solution

Given:

  

  $R^2=87.3\%$

Therefore, 87.3% of the variation between the percentage of Other drugs use and percentage of Marijuana has been explained by the regression model.

e)

To determine

To explain whether the results indicate that marijuana use leads to the use of harder drugs.

Answer to Problem 2E

No.

Explanation of Solution

Given:

  

There could be some lurking variables that influence the relationship. Hence, we cannot say about the effect on the relationship between the variables is due to explanatory variables used.