Question

One of the most widely administered psychological assessments is the Rosenberg Self-Esteem Scale (1965), a 10-item scale that assesses global self-worth by measuring both positive and negative feelings about the self. Scores on this standardized self-esteem questionnaire range from 10-100, with higher scores indicating higher levels of self-esteem. For the general population of American teenagers, the average score is 50 points (SD = 15 points).

1. What is the z-score for Wallace, whose self-esteem score is 46?
2. What is the z-score for Sherman, whose self-esteem score is 57?
3. What is Lando’s self-esteem score, who has a z-score of 2.30?
4. What is Gracie’s self-esteem score, who has a z-score of -0.74?
5. What z-score represents the 10^th percentile?
6. What self-esteem score represents the 10^th percentile?
7. What z-score represents the 80^th percentile?
8. What self-esteem score represents the 80^th percentile?
9. What z-score represents the 25^th percentile?
10. What self-esteem score represents the 99^th percentile?
11. At what percentile is Wallace’s self-esteem score?
12. At what percentile is Sherman’s self-esteem score?
13. What is the probability of scoring higher than Wallace?
14. What is the probability of scoring higher than Sherman?
15. What is the probability of scoring lower than Lando?
16. What is the probability of scoring lower than Gracie?
17. What is the probability of having a self-esteem score between Wallace and Sherman?
18. What is the probability of having a self-esteem score between Wallace and Lando?
19. What is the probability of having a self-esteem score between Wallace and Gracie?
20. What is the probability of having a self-esteem score between Lando and Sherman?

Childhood participation in organizations such as sports, cultural groups, religious groups, and school clubs may be related to improved self-esteem for teens (McGee et al, 2016).

A sample of 100 teens with a history of childhood participation in an organized sport are given the Rosenberg Self-Esteem Scale. Their average score is 55 points.

M = __________               μ = ___________        n = _____________   σ= _____________   σ_M = _____________

1. Find the z-score for this sample mean.
2. At what percentile is this sample?
3. What is the probability of selecting a sample whose mean self-esteem score is greater than this sample?
4. What is the probability of selecting a sample whose mean self-esteem score is less than this sample?

A sample of 25 teens with a history of childhood participation in a cultural organization are given the Rosenberg Self-Esteem Scale. Their average score is 54 points.

M = __________               μ = ___________         n = _____________    σ= _____________   σ_M = _____________

5. Find the z-score for this sample mean.
6. At what percentile is this sample?
7. What is the probability of selecting a sample whose mean self-esteem score is greater than this sample?
8. What is the probability of selecting a sample whose mean self-esteem score is less than this sample?

A sample of 20 teens with a history of childhood participation in a religious club are given the Rosenberg Self-Esteem Scale. Their average score is 48 points.

M = __________               μ = ___________         n = _____________    σ= _____________   σ_M = _____________

9. Find the z-score for this sample mean.
10. At what percentile is this sample?
11. What is the probability of selecting a sample whose mean self-esteem score is greater than this sample?
12. What is the probability of selecting a sample whose mean self-esteem score is less than this sample?

Answer 1