# PSYCH 1110 OU Self Esteem Scores Data Set Raw Score & Z Score Worksheet

A psychologist studied self-esteem scores and found the data set to be normally distributed with a mean of 60 and a standard deviation of 5.

Part A**What raw score cuts off the bottom 33% of this distribution?

Steps:

Q1: What is the z-score that cuts off the bottom 33% of this distribution?

Q2: What is the raw score that cuts off the bottom 33% of this distribution?

Part B**What percentage of the scores is between 65 and 70?

Steps:

Q3: What is the z-score that corresponds to the raw score of 65?

Q4: What is the z-score that corresponds to the raw score of 70?

Q5: What percentage of the scores is between 65 and 70?

Part C:**A raw score of 57.5 is associated with what percentile?

Steps:

Q6: What is the z-score associated with a raw score of 57.5?

Q7: A raw score of 57.5 is associated with what percentile?

Part D:**What raw scores mark the middle 95% of this distribution?

Steps:

Q8: What are the z-scores that mark the middle 95% of this distribution?

Q9: What is the raw score below the mean?

Q10: What is the raw score above the mean?

Part E:**What is the median of this distribution?

Q11: What is the median of this distribution?

The following 9 questions (Q12 to Q20) are conceptual questions based on Modules 3 and 4.

Q12: In a positively skewed distribution, Alice scored the mean, Betty scored the median, and Claire scored the mode. Who had the lowest score?

1. Alice
2. Betty
3. Claire
4. All three scored approximately the same

Q13: In a normal distribution, Alice scored the mean, Betty scored the median, and Claire scored the mode. Who had the lowest score?

1. Alice
2. Betty
3. Claire
4. All three scored approximately the same

Q14: The z-distribution always has a mean of _____ and a standard deviation of _____.

1. 1; 0
2. 0; 0
3. 0; 1
4. 1;1

Q15: A test score of 84 was transformed into a standard score of –1.5. If the standard deviation of test scores was 4, what is the mean of the test scores?

1. 78
2. 89
3. 90 D. 88

Q16: The standard deviation for the sample numbers 8, 9, and 10 is

1. –3.0
2. 0.0

C..67 D. 1.0 Q17: A university administrator randomly selected 10 freshmen and 10 seniors and asked them how satisfied they are with life at Ohio University on a 1 (not at all satisfied) to 9 (very satisfied) scale. The administrator’s date is below:

Mean Variance

Freshmen 3 10

Seniors 8 1

These results seem to indicate that:

1. freshmen agree more with each other about their life satisfaction than do seniors
2. seniors agree more with each other about their life satisfaction than do freshmen
3. all freshman tend to be satisfied with life
4. freshmen and seniors experience equal life satisfaction E. none of the above are accurate

Q18: A sample of data has a standard deviation of 10. If you were to divide all the scores in the date set by a factor of two (2), what would the new standard deviation be?

1. 10
2. 5
3. 2.5
4. none of the above

The following 2 questions (Q19 to Q20) are either “True” or “False”

Q19: The variance for a set of data can be a negative value.

Q20: The two parameters that completely characterize a standardized normal distribution are “μ” and “σ”.