An educational psychologist is interested in knowing whether the experience of attending preschool...

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An educational psychologist is interested in knowing whether the experience of attending preschool is related to subsequent sociability. She identifies two groups of first graders: those who had attended preschool and those who had not. Then each child is assigned a sociability score on the basis of observations made in the classroom and on the playground. The following sociability results are obtained: Attended preschool Did not attend preschool n1 = 12, ?X1 = 204, SS1 = 192 n2 = 16, ?X2 = 248, SS2 = 154 a. Set up the appropriate statistical hypotheses. b.

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9. An educational psychologist is interested in knowing whether the experience of attending preschool is related to subsequent sociability. She identifies two groups of first graders: those who had attended preschool and those who had not. Then each child is assigned a sociability score on the basis of observations made in the classroom and on the playground. The following sociability results are obtained: Attended preschoolDid not attend preschool n1 = 12, ?X1 = 204, SS1 = 192n2 = 16, ?X2 = 248, SS2 = 154 a. Set up the appropriate statistical hypotheses. b. Perform the test (æ = .05) 16. The director of Academic Support services wants to test the efficacy of a possible intervention for undergraduate students who are placed on academic probation. She randomly assigns 28 such students to two groups. During the first week of the semester, students in Group 1 receive daily instruction on specific strategies for learning and studying. Group 2 students spend the same time engaged in general discussion about the importance of doing well in college and the support services that are available on campus. At the end of the semester, the director determines the mean GPA for each group: Group 1 (strategy instruction)Group 2 (general discussion) n1 = 14, X1 = 2.83, S1 = .41n2 = 14, X2 = 2.26, S2 = .39 12. Recall the very low correlation between matched pairs in problem 6 (r12 = +.04). Reanalyze these data as if the scores were from two independent groups of eight participants each. a. Compare the two sets of results with respect to sx1 - sx2, the sample of t ratio, and the appropriate statistical decision. 7. Study the following ANOVA summary, and then provide the missing information for the cells designated a-f: SourceSS dfMSFP Between groups(a) 3(b)(c)(d) Within-groups64 (e)(f) _______________________________________ Total349 19 _______________________________________________________________ 9. a. How...

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David · Accepted Answer

9
9. An educational psychologist is interested in knowing whether the experience of 
attending preschool is related to subsequent sociability.  She identifies two groups of first 
graders: those who had attended preschool and those who had not.  Then each child is 
assigned a sociability score on the basis of observations made in the classroom and on the 
playground.  The following sociability results are obtained:  
Attended preschool    Did not attend preschool 
n1 = 12,  ∑X1 = 204,  SS1 = 192  n2 = 16,  ∑X2 = 248,  SS2 = 154 
a. Set up the appropriate statistical hypotheses. 
b. Perform the test (α = .05) 
Ans: (Note: I assumed SS is sum of squares) 
Here the psychologist wants to see if there is a difference between the scores due to 
attending preschools. Let μ1 and μ2 are the population mean of scores of the 
graders who attended preschool and did not consecutively. 
Null Hypothesis: 
So the hypothesis of interest is, 
Ho: μ1 = μ2 against Ha: μ1 ≠ μ2 
Or equivalently, 
Ho: μ1 - μ2 =0 against Ha: μ1 - μ2 ≠ 0 
Test statistic  
Here we don’t know the sample variance thus we will use the t test to test the 
hypothesis. Assuming unequal variance for the populations the test statistic can be 
given by, 
21
21
2
2
2
1
21
n
s
n
s
XX
t











 ; Under the null hypothesis this t follows a t-distribution 
with appropriate degrees of freedom. 
The degrees of freedom can be calculated using the formula, 
 Degrees of freedom=
   
12
2/
11
1/
21
22
2
22
1
2
2
2
2
1











n
ns
n
ns
n
s
n
s
v  
Rejection Condition: 
Since under the null hypothesis t follows a t distribution so deviation from null 
hypothesis implies deviation from t-distribution or vice versa. Again if we look at 
the alternative we can see it is both sided thus the considered test is a two tail test 
and we will reject the null hypothesis at 100α% level of significance if, 
Observed |t| > tv,α/2
Calculation: 
From the given values, 
Mean of 1
st
 sample = 204/12 = 17 
Mean of 2
nd
 sample =248/16 = 15.5 
Sample variance of 1
st
 sample = SS1/(12-1) = 17.45 
So standard deviation of 1
st
 sample = 4.18 
Sample variance of 2
nd
 sample = 154/15 = 10.27 
Standard deviation of 2
nd
 sample= 3.

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