chapt 5 practices NIBRS-GSS / CJ STATS
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SPSS5Lecture.pptx
GSS and NIBRS 5 Lecture
Dr. M. Spencer
How to Calculate a Z Score
It is possible to determine the area under the curve for any sigma distance from the mean.
This distance is called a z score.
Indicates direction and distance that any raw score deviates from the mean in sigma units
Using z Scores to Calculate Probability
When the normal curve is used in conjunction with z scores and Table A in Appendix C, we can determine the probability of obtaining any raw score (X) in a distribution.
The converse, addition, and multiplication rules still apply.
Using Table A and your z score:
If the score is less than the mean, look up the z score in Table A.
Then subtract the number in column B from 50.
Convert to a decimal
If the score is more than the mean, look up the z score in Table A.
Then add the number in column B to 50.
Convert to a decimal.
GSS 5 – Question 1
Education is an important issue. Using the General Social Survey, find the mean and standard deviation for the highest year of school completed (EDUC).
Using this mean and standard deviation, what percentage of Americans are expected to complete 16 or more years of education (16 or above)?
What percentage of Americans are expected to report 10 or fewer years as their highest year of school completed?
Education
GSS 5 – Question 2
Using the frequencies procedure (ANALYZE, DESCRIPTIVE STATISTICS, FREQUENCIES), request a histogram of television viewing data from the General Social Survey (TVHOURS) with the normal curve overlay (from the Charts button), as well as the mean and standard deviation (from the Statistics button).
Comment on the closeness of the actual distribution to the normal curve.
Based on the normal distribution (using the z score and Table A), what is the probability that a person watches 3 or more hours of television per day?
Hours of TV per Day
GSS 5 – Question 3
Using the frequencies procedure (ANALYZE, DESCRIPTIVE STATISTICS, FREQUENCIES), request a histogram of total family income (INCOME06) from the General Social Survey with the normal curve overlay (from the Charts button), as well as the mean and standard deviation (from the Statistics button).
Comment on the closeness of the actual distribution to the normal curve.
Based on the normal distribution (using the z score and Table A), what is the probability that a family has an income of $75,000 to $89,000 (21 on the scale)?
Family Income
NIBRS 5 – Question 1
Find the mean and standard deviation for offender age.
Using the mean and standard deviation, what percentage of offenders are over 18?
What percentage of offenders are over 21?
What is the probability of selecting at random an offender who is under 18?
Offender Age - Assaults
NIBRS 5 – Question 2
Using the frequencies procedure (ANALYZE, DESCRIPTIVE STATISTICS, FREQUENCIES), request a histogram of victim age with the normal curve overlay (from the Charts button), as well as the mean and standard deviation (from the Statistics button).
Comment on the closeness of the actual distribution to the normal curve.
Based on the normal distribution (using the z score and Table A), what is the probability that a victim is under 13?
Victim Age - Assaults
NIBRS 5 – Question 3
Using the frequencies procedure (ANALYZE, DESCRIPTIVE STATISTICS, FREQUENCIES), request a histogram of offender age with the normal curve overlay (from the Charts button), as well as the mean and standard deviation (from the Statistics button). Comment on the closeness of the actual distribution to the normal curve.
Offender Age - Assaults
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mean of a distribution
standard deviation of a distribution
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