Hypothesis Testing, Regression Coefficient and Relationship

Please see attached file for full problem description.

A researcher wants an answer to the following question: Does the correlation of .34 between extracurricular activities and academic achievement represent a true relationship. The null hypothesis is there is no relationship between extracurricular activities and academic achievement. The alternative hypothesis is there is a positive relationship between extra curricular activities and academic achievement.

1. Ho: = 0.00
H1: > 0.00

2. Distribution: t ; n = 28

3. a: = .05

4. T.S. ; t = 1.843

5. df: ? , Significance level: .043

6. Decision: ?

1: What are the df (degrees of freedom)? Please show the formula, then show again with numbers filled in and answer reached.

2: What is the probability that the r of .34 occurred by chance?
My answer: Would the answer be 4.3% because the sig. level is .043 ??

3: Indicate whether the obtained r of .34 represents and true or false relationship, and if appropriate, interpret in terms of the coefficient of determination.

4: What does an unstandardized regression coefficient of 1.3 mean in terms of the independent and dependent variables?

5: What statistical test is an extension of the dependent t test when one group is assessed 3 or more times?

2.

A teacher seeks an answer to the problem: Does journal-writing result in more mathematics achievement than no journal writing? Null hypothesis states: There is no difference in mathematics achievement between students who engage in journal writing and students who do not engage in journal writing. The alternative hypothesis states that there is a difference in mathematics achievement between students who engage in journal writing and students who do not engage in journal writing. At the end of the experiment, the journal writing group (group 1) has a mean test score of 43 and the no journal writing group (group 2) has a mean score of 39.

1. Ho: u1=u2
H1: u1 is not equal u2.

2. Distribution: t ; n1 = 16, n2 = 13

3. a: = .05

4. T.S. : t = 1.932

5. df : ? , Significance level = .083

6. Decision: ?

6: What is df (degrees of freedom)? Show formula and how to obtain answer.

7: What is the probability that the difference in the scores could be attributed to chance factors (i.e. sampling error)?
My answer: 8.3%, because the sig. level is .083. CORRECT?

8: What overall conclusion about efficacy of journal writing and no journal writing is warranted from the results?