Question

  

1. A juvenile probation officer is looking at the relationships between number of prior police contacts and continued offending among juveniles who participated in a boot camp. Use the data below to establish hypotheses and calculate the correlation for the relationship between number of prior police contacts and instances of continued offending. State the decision with regard to whether the H₀ is ultimately rejected or retained.

Number of Prior Police Contacts (X)	Number of Offenses (Y)
3	3
4	6
7	5
1	0
0	1
0	2
5	6
3	4

Step 1: State the H₀ and the H₁.

Step 2: Identify the distribution and compute the df.

The distribution is the t distribution.

df =

Step 3: Identify the critical value of the test statistic and state the decision rule.

α = .05

            two-tailed test of significance

critical value =

Step 4: Compute the obtained value of the test statistic

Number of Prior Police Contacts (x)	Number of Offenses (y)	xy	x2	y2
3	3
4	6
7	5
1	0
0	1
0	2
5	6
3	4
Sx =	Sy =	Sxy =	Sx2 =	Sy2=

Step 5: Make a decision about the null and state the substantive conclusion.

Decision Rule:

Reject null if:

t_obt is less than t_crit.

OR

t_obt is greater than t_crit     

2. How strong is the relationship and how much variance is explained?

Use sign, magnitude and Coefficient of Determination (r²)

Sign

Magnitude

• r =

A very general guideline is that values between 0 and

• ±.29 are weak, from about
• ±.30 to ± .49 are moderate,
• ±.50 to ±.69 are strong, and those
• beyond ±.70 are very strong.

Coefficient of Determination

• R² = ___; about ____ % of the variance in the DV (continued offending) can be explained by the IV(# of police contacts).

Answer 1