Question

In a survey of youth in southern Minnesota, the following correlations and p value results were found when the students were asked why they were changing schools: n = 175 (df = 173). α = .05. Assume the study is two-tailed, only interested in whether a relationship exists.

Measures of Correlation for the Desire to Change Schools	Correlation (r ) with Significance
Number of fights in the last year	.567, p < .05
Number of students arrested in the last year	.878, p < .01
Alcohol Abuse	-.167, p > .05
Drug Abuse	-.627, p < .05

Based on the Correlation Coefficients with Significance, answer items 1-6:

1.  Is the relationship for the variable Alcohol Abuse statistically significant ?

2 .For the variable Drug Abuse, would the null hypothesis be rejected?

3.What type of relationship exists for the variable Number of students arrested?

A) strong, inverse

B) moderate, inverse

C) weak, direct

D) strong, direct

4. What type of relationship exists for the variable Drug Abuse?

A) moderate, inverse

B) strong, direct

C) weak, direct

D) strong inverse

5. Based on the relationship indicated between Drug Abuse and the Desire to Change Schools, which is the most appropriate interpretation of r?

	A.	As drug abuse in the school increases, so to does the desire to change schools.
	B.	As drug abuse in the school increases, the desire to change schools decreases.
	C.	Not enough information to interpret

6. What would the coefficient of determination be for the variable Number of Fights?

	A.	0.321
	B.	- 0.627
	C.	0.567
	D.	0.792

Answer 1

The significance level of the test hypothesis is,

The null and alternative hypothesis are defined as,

The decision rule state that if,

1.

From the test result table,

Measures of Correlation for the Desire to Change Schools	Correlation (r ) with Significance
Alcohol Abuse	-.167, p > .05

Since the P-value is greater than 0.05 at 5% significance level, the null hypothesis is not rejected. Hence there is no significant correlation is between Desire to Change Schools and Alcohol Abuse.

2.

From the test result table,

Measures of Correlation for the Desire to Change Schools	Correlation (r ) with Significance
Drug Abuse	-.627, p < .05

Since the P-value is less than 0.05 at 5% significance level, the null hypothesis is rejected. Hence there is a significant correlation is between Desire to Change Schools and Drug Abuse.

3.

Answer: D) strong, direct

Explanation: From the test result table,

Measures of Correlation for the Desire to Change Schools	Correlation (r ) with Significance
Number of students arrested in the last year	.878, p < .01

The correlation coefficient value between 0.8 and 1 indicates the strong positive(direct) correlation between hence there is a strong direct correlation between Desire to Change Schools and Number of students arrested in the last year

4.

Answer: A) moderate, inverse

Explanation: From the test result table,

Measures of Correlation for the Desire to Change Schools	Correlation (r ) with Significance
Drug Abuse	-.627, p < .05

The correlation coefficient value between -0.5 and 0.8 indicates the moderate negative(inverse because negative r) correlation between hence there is a moderate inverse correlation between Desire to Change Schools and Drug Abuse.

5.

Since there is a moderate inverse correlation between Desire to Change Schools and Drug Abuse and the correlation coefficient is significant at 5% significant level, we can conclude that as the number of Drug Abuse increases, the Desire to Change Schools decreases.