Homework 5 Z-Scores – What are always the mean and standard deviation of the z-distribution?

Homework 5

Z-Scores

Be sure you have reviewed this module/week’s lessons and presentations along with the practice data analysis before proceeding to the homework exercises. Complete all analyses in SPSS, and then copy and paste your output and graphs into your homework document file. Number all responses. Answer any written questions (such as the text-based questions or the APA Participants section) in the appropriate place within the same file. Review the “Homework Instructions: General” document for an example of how homework assignments must look.

 

Part I: Concepts

These questions are based on the Nolan and Heinzen reading and end-of-chapter questions.

 

1. What are always the mean and standard deviation of the z-distribution?

2. Define the central limit theorem.

3. Fill in the blanks: A z-score is based on a distribution of _____________, while a z-statistic is based on a distribution of __________________.

4. End-of-chapter problems: 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.

· Raw and z-scores: 6.16 and 6.20

· Estimating percentages under normal curve: 6.27

· Distribution of means and z-statistic: 6.28 and 6.30

 

Part II: SPSS Analysis

1. Green and Salkind, Lesson 21, Exercise 1

Open the “Lesson 21 Exercise File 1” document (found in the course’s Assignment Instructions folder) in order to complete these exercises.

a. Create a histogram of the anxiety raw scores and paste it into your homework document.

b. 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 your homework document. These descriptive statistics should describe the original raw scores and not the new z scores.

c. Remember that the mean of a standard normal distribution is z = 0 and the standard deviation is 1. What is the z-score that is closest to 0 (on either side of the mean) in your data set? What is the z-score that is the farthest from 0 (on either side of the mean) in your data set?

 

 

d. Based on the histogram from (a) and the answers to (c), 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

1. The following data 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.

a. Generate descriptive statistics and a histogram for this variable. Based on the data and graph, choose 1 measure of central tendency and 1 measure of dispersion (variability) that best describes the data set. Justify why you chose these measures in a statement beneath the output.

b. 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 60? To a raw IQ score of 104?

c. 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

1. (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®.

a. What is the independent variable in this experiment?

b. What is the dependent variable?

c. What is the likely null hypothesis for this experiment?

d. What is the likely research hypothesis for this experiment?

 

2. (Non-SPSS) A clinical psychologist wants to test a new long-term treatment program for people diagnosed with bipolar disorder. She assigns 20 participants to the new treatment program and 20 participants to a standard treatment program.

a. State the likely null hypothesis for this study.

b. State the likely research hypothesis for this study.

 

3. (SPSS) A criminal psychologist wants to examine the level of narcissistic personality traits between those who are diagnosed with antisocial personality disorder (ASPD) and those who do not qualify for ASPD. She administers a measure of narcissistic personality traits where higher scores indicate higher levels of narcissism and scores range from 0–35.

 

a. 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. 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, enter No ASPD Diagnosis information as:

Continue in this fashion to the end of the file.

b. 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). Paste this into your homework document.

c. Construct a boxplot to show the difference between the mean scores of the 2 groups.

 

 

Submit Homework 5 by 11:59 p.m. (ET) on Monday of Module/Week 5.