1. Suppose you are directing an agency that provides services to children with t
ID: 3052103 • Letter: 1
Question
1. Suppose you are directing an agency that provides services to children with trauma. You know that some therapists use directive therapeutic methods while others use non-directive. You want to know which method works better.
a). So, you do two tests. In the first test, you want to find out if all children who come into the agency are improving? So, first, you assess all children upon intake for their levels of aggression since you know that children who experience trauma may exhibit aggressive behavior. After 6 weeks you test them again on aggression to see if they have improved. Go through all of the steps of hypothesis testing. The data are in the table below:
Scores on aggressive behavior in children from intake through 6 weeks of treatment. *Higher scores indicate higher levels of aggression
Score on pretest
Score on posttest
13
12
9
9
8
5
11
11
7
4
12
10
15
14
9
7
10
10
11
12
b) Second, you want to see which treatment method works better, directive or non-directive. So, you randomly assign a different group of children into two groups. One group receives directive treatment and the other receives non-directive treatment. You measure them after 6 monhts of treatment at posttest on aggressive behavior. Go through all of the steps of hypothesis testing. Their scores are below:
Scores on posttest after 6 months of group therapy. Higher scores indicate higher levels of aggression.
Directive Treatment
Non-directive Treatment
13
11
10
6
14
15
12
9
10
12
8
6
12
9
9
9
13
9
10
6
For both, conduct the appropriate tests at alpha = .05 for each data set above. Use the appropriate hypothesis test and go through all steps of testing. Be sure to interpret using means, your test statistic, p values, and words.
2) As a researcher, you are examining county data in your state to find out if the rate of deaths from traffic accidents may be the result of the percent of the population of that county that is comprised of males aged 16 to 21. Table 13 below displays the data from a sample of 15 counties across your state.
Table 13: Rate of deaths due to traffic accidents and percent of the population that consists of males ages 16 to 25
County
Rate of Traffic Deaths
% of Population Young Males
Jefferson
15
4
Lincoln
16
5
Franklin
22
10
Fayette
23
9
Washington
20
8
Lewis
25
11
Cole
18
2
Cheyenne
15
6
Adams
19
12
Banks
10
3
Charles
9
2
Frederick
18
15
Warren
15
9
Harding
24
16
Poland
9
3
a) A researcher speculates that localities with high percentages of young male drivers would have more traffic-related fatalities. Test the relationship between traffic deaths and percent of the population that is young and male. Identify the independent and dependent variables. Draw a scatterplot.
b) What is the least squares regression line for these data? Interpret the slope coefficient. (You will need to enter the data into SPSS as 2 variables.) Identify 2 points on the line and draw it on the plot you made above.
c) Identify the value of the correlation coefficient for these two variables. Discuss the strength and direction of the relationship.
d) Find the coefficient of determination and explain what it means.
e) What is the predicted rate of traffic deaths from a county that 15 percent of the population as young males? What is the observed rate of traffic deaths for a county with 15 percent of the population as young males? What is the residual?
Score on pretest
Score on posttest
13
12
9
9
8
5
11
11
7
4
12
10
15
14
9
7
10
10
11
12
Explanation / Answer
Question 1
Step 1 : Hypothesis testing
H0 : There is no change in the agresssion score of children after 6 weeks of training at the agency. 1 = 2
H1 : There is significant reduction in the agression score after 6 weeks of training at the agency. 1 > 2
Here 1 represents pretest treatment and 2 represents posttest treatment.
Step2 : Significane level of testing alpha = 0.05
Step 3 : Critical value of Test statistic
dF = 10 + 10 -2 = 18
tcritical = t18,0.05 = 1.7361 (one tailed)
Step 4 : Test statistic
Pooled Standard deviation sp = sqrt [(s12 + s22)/2] = sqrt [(2.41522 + 3.20422)/2] = 2.8373
Here test statistic
t = (x1 - x2)/[sp * sqrt (1/n1 + 1/n2)] = (10.5 - 9.4)/ [2.8373 * sqrt (1/10 + 1/10)] = 0.867
Here p - value = TDIST (0.867; 18 ; 0.05) = 0.1987
Step 5 : The conclusion
Here we failed to reject the null hypothesis so we can conclude tha there is no significant reduction in agression score of students after joining the agency 6 week course.
(b)
Step 1 : Hypothesis testing
H0 : Both type of treatments are same effective ; Directive Treatment is similar to the non directive treatment at the agency. 1 = 2
H1 : Non Directive Treatment is better to the directive treatment at the agency. 1 > 2
Here 1 is for directive treatment and 2 is non- directive treatment.
Step2 : Significane level of testing alpha = 0.05
Step 3 : Critical value of Test statistic
dF = 10 + 10 -2 = 18
tcritical = t18,0.05 = 1.7361 (one tailed)
Step 4 : Test statistic
Pooled Standard deviation sp = sqrt [(s12 + s22)/2] = sqrt [(1.96922 + 2.89832)/2] = 2.4777
Here test statistic
t = (x1 - x2)/[sp * sqrt (1/n1 + 1/n2)] = (11.1 - 9.2)/ [2.4777* sqrt (1/10 + 1/10)] = 1.7147
Here p- value = TDIST (1.7147 ; 18) = 0.052 > 0.05
step 5 :
Here we failed to reject the null hypotheis as t < tcriticall so we can conclude that there is no significant difference in directive treatment and non directive treatment.
Score on pretest Score on posttest 13 12 9 9 8 5 11 11 7 4 12 10 15 14 9 7 10 10 11 12 Average 10.5 9.4 Std. Dev. 2.4152 3.2042Related Questions
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