LASA 2: Conducting and Analyzing Statistical Tests
By Saturday, December 15, 2012, post your...

Question

LASA 2: Conducting and Analyzing Statistical Tests
 By Saturday, December 15, 2012, post your results to the M5: Assignment 1 Dropbox.Your
 written presentation to the following problem situation should be a 
formal academic presentation wherein APA guidelines apply.
 A study wants to examine the relationship between student
 anxiety for an exam and the number of hours studied. The data is as 
follows:

Student Anxiety Scores

Study Hours

5

1

10

6

5

2

11

8

12

5

4

1

3

4

2

6

5

1

2

Why is a correlation the most appropriate statistic?
 What is the null and alternate hypothesis?
 What is the correlation between student anxiety 
scores and number of study hours? Select alpha and interpret your 
findings. Make sure to note whether it is significant or not and what 
the effect size is.
 How would you interpret this?
 What is the probability of a type I error? What does this mean?
 How would you use this same information but set it up in a way that allows you to conduct a t-test? An ANOVA?

Assignment 1 Grading Criteria
 
 Maximum Points

Explain why a correlation is the most appropriate statistic.
 
 36

List the null and alternate hypothesis.
 
 20

Compute and correctly present the correlation between student anxiety scores and number of study hours.
 
 36

List the alpha, statistical significance of the results and the effect size. Provide an interpretation of the results.
 
 60

List the probability of a type I error and explain what it means.
 
 36

Explain how the same information would be set up to allow one to conduct a t-test and an ANOVA.
 
 48

Writing Components:
 Organization: Introduction, Thesis, Transitions, Conclusion
 Usage and Mechanics:Grammar, Spelling, Sentence structure
 APA Elements: Attribution, Paraphrasing, Quotations
 Style: Audience, Word Choice

64

Total:
 
 300

Robert · Accepted Answer

1) Correlation tells us about the dependency of two or more variables. As we know in real 
life there are many variables present which depends on other factors. As for example 
income and expense of a person, while considering these kinds of variables or rather 
when we want to check for dependency of two variables we use the correlation. And as a 
measure of correlation or dependency we use the correlation coefficient which varies in 
between -1 to 1 for a bivariate case (i.e. considering only two variable) or 0 to 1 for a 
multivariate case (i.e. for more than 2 variables). Higher the correlation higher is the 
dependency. 
Now here the considered study wants to examine the relationship between student anxiety 
for an exam and the number of hours studied. We all know students study more if they 
are more anxious about the exam. A relaxed student (in general) studies lot less than a 
serious student. So there is definitely a relationship or dependency present for these two 
variables “Student Anxiety Score” and “Study hours”. So from the previous discussion 
we can say that here the correlation is the most appropriate statistic cause the researcher 
wants to see the relationship in between the considered variables.
2) Now here the study wants to see the dependency in between the considered variables 
“Student Anxiety Score” and “Study hours”. So the obvious two outcomes should be 
“There is a dependency present” and “there is no dependency present”. A null hypothesis 
is that hypothesis between the two which is more unbiased and more serious i.e. rejection 
of which may lead to serious damage. So considering all these facts, and assuming   is 
the population correlation the null and alternative hypothesis can be given as, 
H0 :     against Ha :    .
3) Let Xi denotes the anxiety score and Yi denotes the study hours for the ith student then 
the correlation coefficient can be written as, 
r = Corr(X,Y) = 
        
          
 
Now, 
Cov(X,Y) =  (Xi-  ̅)(Yi-  ̅) and from the given data, 
Cov(X,Y) = 4.7. 
Sd(X) = √         = √          = 3.84274 and 
Sd(Y) = = √         = √         = 2.404 
So , 
r = 4.7/(3.84274*2.404) = 0.56371. 
So the correlation coefficient is positive (as expected) and moderately high. 
But to be sure we need to test the hypothesis of correlation.

LASA 2: Conducting and Analyzing Statistical Tests By Saturday, December 15, 2012 , post your results to the M5: Assignment 1 Dropbox. Your written presentation to the following problem situation...

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Student Anxiety Scores	Study Hours
5	1
10	6
5	2
11	8
12	5
4	1
3	4
2	6
6	5
1	2

Assignment 1 Grading Criteria	Maximum Points
Explain why a correlation is the most appropriate statistic.	36
List the null and alternate hypothesis.	20
Compute and correctly present the correlation between student anxiety scores and number of study hours.	36
List the alpha, statistical significance of the results and the effect size. Provide an interpretation of the results.	60
List the probability of a type I error and explain what it means.	36
Explain how the same information would be set up to allow one to conduct a t-test and an ANOVA.	48
Writing Components: Organization: Introduction, Thesis, Transitions, Conclusion Usage and Mechanics:Grammar, Spelling, Sentence structure APA Elements: Attribution, Paraphrasing, Quotations Style: Audience, Word Choice	64
Total:	300