## PSYC 354 Homework 5

1)

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

Answer (mean)

Answer (standard deviation)

2)

Define the central limit theorem.

Answer

3)

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

Work:

4b) X = 231; Z = Answer

Work:

4c) X = 179; Z = Answer

Work:

4d) X = 163; Z = Answer

Work:

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

Work:

5b) Z = -2.44; X = Answer

Work:

5c) Z = -1.0; X = Answer

Work:

5d) Z = 1.83; X = Answer

Work:

6) In a normal curve, what percentage of scores falls:

6a) Above the mean? Answer

Work:

6b) Between -1 and +1 standard deviations (SD) from the mean? Answer

Work:

6c) Beyond 2 SD’s away from the mean (in the tails on both sides)? Answer

Work:

6d) Between the mean and 2 SD’s above the mean? Answer

Work:

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

Work:

7b) 140 Answer

Work:

7c) 1400 Answer

Work:

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

Work:

8b) A sample of 80 scores has a mean of 95 Answer

Work:

8c) A sample of 50 scores has a mean of 100. Answer

Work:

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.

Part II:

Exercises 1a-1d

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.

1a)

Create a histogram of the anxiety raw scores and paste it below.

Answer: Histogram

1b)

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

1c)

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?

Answer

Answer

1d)

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.

Answer

Justification

Part III: SPSS Data Entry and Analysis

Data provided below.

IQ Scores

79

120

104

145

108

100

115

107

60

122

105

87

98

124

82

93

89

123

117

104

112

96

88

98

105

91

113

123

124

90

Part III:

Questions 1a-1e

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.

1-a)

Generate descriptive statistics for this variable.

Answer: Descriptive Statistics Table

1-b)

Generate a histogram for this variable.

Answer: Histogram

1-c)

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?

115

Answer

79

Answer

107

Answer

1-d)

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?

Answer

Justification

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®.

1-a)

What is the independent variable in this experiment?

Answer

1-b)

What is the dependent variable?

Answer

1-c)

What is the likely null hypothesis for this experiment?

Answer

1-d)

What is the likely research hypothesis for this experiment?

Answer

ASPD

Diagnosis

No ASPD

Diagnosis

30

12

20

21

27

9

17

27

34

32

9

8

18

12

6

5

8

14

10

4

Part IV:

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:

Column 1

Column 2

“Diagnosis”

“Score”

1

23

1

11

1

19

• 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:

Column 1

Column 2

2

10

2

8

2

19

[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

2-a)

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]

2-b)

Construct a boxplot to show the difference between the mean scores of the 2 groups. (3 pts)

Answer: Boxplot