What are always the mean and standard deviation of the z-distribution?
Answer (standard deviation)
Define the central limit theorem.
Fill in the blanks: A z-score can be thought of as the number of ________ that a score is from the mean.
Part I: Questions 4-8
Remember to show work to receive partial credit where applicable. For help working on these problems, refer to the presentation from this module/week on the normal curve and computing z-scores.
4) Calculating z scores from raw scores: If a population has a mean of =198 and a standard deviation of = 20, calculate z scores for each of the following raw scores (X) from this population. Show work on the right hand side, put answers on the left in the space provided.
4a) X = 210; Z = Answer
4b) X = 231; Z = Answer
4c) X = 179; Z = Answer
4d) X = 163; Z = Answer
5) Calculating raw scores from z scores: If a population has a mean of =198 and a standard deviation of = 20, calculate raw scores (X) for each of the following z scores from this population. Show work on the right hand side, put answers on the left in the space provided.
5a) Z = .56; X = Answer
5b) Z = -2.44; X = Answer
5c) Z = -1.0; X = Answer
5d) Z = 1.83; X = Answer
6) In a normal curve, what percentage of scores falls:
6a) Above the mean? Answer
6b) Between -1 and +1 standard deviations (SD) from the mean? Answer
6c) Beyond 2 SD’s away from the mean (in the tails on both sides)? Answer
6d) Between the mean and 2 SD’s above the mean? Answer
7) Compute the standard error (m) for each of the following sample sizes, assuming a population mean of 125 and a standard deviation of 20.
7a) 40 Answer
7b) 140 Answer
7c) 1400 Answer
8) Compute a z-statistic for each of the following sample means, assuming the population has a mean of 100 and a standard deviation of 30 (Remember to compute M before computing the z statistic!)
8a) A sample of 32 scores has a mean of 113 Answer
8b) A sample of 80 scores has a mean of 95 Answer
8c) A sample of 50 scores has a mean of 100. Answer
Part II: SPSS Analysis
Module 5 Lesson 21 Exercise File 1
Open the “Lesson 21 Exercise File 1” document (found in the course’s Assignment Instructions folder) in order to complete these exercises.
Use file: Module 5 Lesson 21 Exercise File 1
Using the data set (answers will be pasted into the blanks below this summary):
• a) Create a histogram of the raw scores
• b) Transform the raw scores to z-scores
o Label the new variable “z_anxiety”
• Paste Descriptive Statistics Table of the raw anxiety scores
o Note that descriptive statistics should describe the original raw scores and not the new z scores
• c) Identify the z-score that is closest to 0 and farthest from 0.
• d) Evaluate whether the scores are normally distributed.
o Support your answer.
Create a histogram of the anxiety raw scores and paste it below.
Using the descriptives method covered in the presentation and chapter, transform the anxiety raw scores to z-scores, creating a new variable called “z_anxiety.”
Paste the output of descriptive statistics in the cell below.
These descriptive statistics should describe the original raw scores and not the new z-scores.
Answer: Descriptive Statistics Table
What is the z-score that is closest to 0 (on either side of the mean) in the data set?
What is the z-score that is the farthest from 0 (on either side of the mean) in the data set?
Based on the histogram from (1a) and your other answers above, would you describe the anxiety data as being normally distributed? Why or why not? Support your answer with information from the chapter and presentations regarding normal and standard normal z-distributions.
Part III: SPSS Data Entry and Analysis
Data provided below.
The data in the columns to the left represent IQ scores of a sample of 30 high school students. In the general population, IQ scores have a mean of 100 and a standard deviation of 15. Enter this data into SPSS. Be sure to save this file, since you will be using it next week as well.
• Generate descriptive statistics for this variable.
• Generate a histogram for this variable.
• In your data set, standardize the IQ scores by transforming them into z-scores
o Label the new variable “ZIQ”
• Which z-scores corresponds to a raw IQ score of 115, 79 and 107?
• Does the distribution reflect the distribution in the general population?
o Support your answer.
Generate descriptive statistics for this variable.
Answer: Descriptive Statistics Table
Generate a histogram for this variable.
In your data set, standardize the IQ scores by transforming them into z-scores under a new variable “ZIQ.”
Using your data set as a reference, what z-score corresponds to a raw IQ score of 115?
To a raw IQ score of 79? To a raw IQ score of 107?
Based on what you have been told about IQ scores in the beginning of the problem,
does this sample’s distribution seem to reflect the distribution of IQ scores in the general population?
Why or why not?
Part IV: Cumulative
Data provided below for respective questions.
Part IV: Question 1a-1d (Non-SPSS)
A cognitive psychologist wants to find out whether playing Minecraft® affects fourth graders’ scores on a visuospatial task.
He assigns 30 fourth graders to 1 of 2 groups.
Group 1 plays Minecraft® for 20 minutes, then completes the visuospatial task.
Group 2 completes the visuospatial task without playing Minecraft®.
What is the independent variable in this experiment?
What is the dependent variable?
What is the likely null hypothesis for this experiment?
What is the likely research hypothesis for this experiment?
Questions 2a & 2b (SPSS)
A forensic psychologist wants to examine the level of narcissistic personality traits in those who are diagnosed with antisocial personality disorder (ASPD) and those who do not qualify for ASPD within a local prison population. She administers a measure of narcissistic personality traits where higher scores indicate higher levels of narcissism and scores range from 0–35.
• Create a new SPSS data file for these scores.
• Your file must have 2 variables: Diagnosis and Score.
• Your diagnosis variable must be set up as a 1-column grouping variable with 2 groups (diagnosis, no diagnosis) coded numerically. This will be much like the gender variable you created in a previous module/week.
o For example, if you code ASPD Diagnosis as 1 and No ASPD Diagnosis as 2, then the SPSS file will appear somewhat like the following:
• All ASPD Diagnosis scores from the table above will appear in a similar fashion.
• Then, continuing in the same columns, enter No ASPD Diagnosis information as:
[Continue in this fashion to the end of the file]
• a) Compute descriptive statistics by diagnosis (that is, for each of the two groups in one table) using similar steps to those covered in Green and Salkind’s Lesson 21 and in the Module/Week 3 presentation (HS GPA scores by Gender).
• b) Construct a boxplot to show the difference between the mean scores of the 2 groups
Compute descriptive statistics by diagnosis (that is, for each of the two groups in one table) (2 pts)
Answer: SPSS Table- Descriptive Statistics for Score (level of narcissistic personality) grouped by Diagnosis (ASPD/No ASPD):
[Paste one table]
Construct a boxplot to show the difference between the mean scores of the 2 groups. (3 pts)