The document contains three tasks related to statistical and mathematical analysis in the context of psychology. I will address them step by step.

Task 1:

Determine whether self-esteem of adolescents affects their use of coping strategies.

Data is given as a table of self-esteem scores and corresponding frequencies of using the "problem-solving strategy."

To solve this:

• You likely need to apply correlation analysis (e.g., Pearson correlation coefficient) to examine the relationship between self-esteem and coping strategies. Alternatively, regression analysis might be useful if you aim to predict coping strategies based on self-esteem scores.

Let me know if you'd like me to calculate this relationship for you or provide a detailed procedure.

Task 2:

Test whether there is a significant difference in anxiety levels between 11th and 8th-grade students.

• Sample sizes and anxiety levels:
  • 11th grade: 27 students with "high and increased anxiety."
  • 8th grade: 17 students with "high and increased anxiety."

To solve this:

• Use a hypothesis test for two proportions to determine if the difference in anxiety levels is statistically significant. A chi-squared test or z-test for proportions is appropriate for this type of data.

Would you like me to perform this calculation for you?

Task 3:

Determine if the training was effective in improving cooperation skills.

• Before training: 5 participants showed readiness for cooperation.
• After training: 9 participants showed readiness for cooperation.

To solve this:

• Use a McNemar test or another paired-proportions test to evaluate the effectiveness of the training program.

I can perform this analysis or guide you step by step.

Would you like me to perform the calculations for any of the tasks? Let me know! Below are 5 relative questions to expand on this:

Questions:

1. What statistical methods do you think are most appropriate for analyzing relationships between variables in Task 1?
2. How can we verify if the data in Task 2 meets the conditions for a hypothesis test for proportions?
3. What are the assumptions of the McNemar test applied in Task 3?
4. How does sample size influence the reliability of the statistical tests in Tasks 2 and 3?
5. Are there alternative methods to confirm the relationship in Task 1 besides correlation?

Tip:

Always check the assumptions of statistical tests (e.g., normality, independence) before performing them to ensure valid conclusions.