# math/ statics

 Work hard to make certain that the results you have are accurate based on class material. Use T- table and Z-table when needed. Feel free to consult and cite the notes and previous assignments in preparing this exam.   Please show all of your working out so I am able to see your path to your answer. Mistakes will be penalized however showing your working out will allow me to deduct fewer points. If no working out is shown, I will be forced to deduct full points for mistakes.   **   . Z table and T table are attached. Please read carefully!

When appropriate and possible, express your answer in the same units as the variable.  For example, if the question asks for the mean years of formal education and you have calculated the mean to be 18.44, your answer should be expressed as â€œ18.44 years of formal education.â€

Equations to Use

Median Position = N+1/2

The Median Value is the midpoint between the scores.

Mean = Ã¥ x   / N

Standard Deviation =

Z score =  x â€“ mean / standard deviation

CI = For samples sizes â‰¥ 100, the formula for the CI is:

CI = Â­(the sample mean) + & – Z(s / âˆšN â€“ 1)

CI = For samples sizes < 100, the formula for the CI is:

CI = Â­(the sample mean) + & – T(s / âˆšN â€“ 1)

1. You are interested in the effects of release with aftercare for a small number of drug offenders. The number of additional months without drug use for a sample of 6 offenders is recorded. The data on the six (6) subjects are as follows:

2     8    5    2     8     2

1. What are the median position and the median value? (3 points)

2. What is the mean? (2 points)

3. What is the most frequently occurring score in this distribution of scores – mode? (2 point)

2. Computation of a mode is most appropriate when a variable is measured at which level? (2 points)

A. interval-ratio

B. ordinal

C. nominal

D. discrete

3.  Assume that the distribution of a college entrance exam is normal with a mean of 500 and a standard deviation of 100. For each score below, find the equivalent Z score, the percentage of the area above the score, and the percentage of the area below the score. ( 5 each = total 10 points)

Score                                   Z score                  % Area Above             % Area Below

a) 437

b) 526

4. The class intervals below represent ages of respondents. Which list is both exhaustive and mutually exclusive? (2 points)

A. 119â€“120, 120â€“121, 121â€“122

B. 119â€“120, 121â€“122, 123â€“124

C. 119â€“121, 123â€“125, 127â€“129

D. 119â€“120, 122â€“123, 125â€“126

5. The parole board is alarmed by the low number of years actually spent in prison for those inmates sentences to 15-year sentences. To help them make parole recommendations they gather data on the number of years served for a small sample of 7 (seven) potential parolees. The number of years served for these seven parolees is as follows:

4

5

3

6

3

3

7

What is the standard deviation for this distribution? (6 points)

6. A teacher gives the following assignment to 200 students: Check the local newspaper every morning for a week and count how many times the word â€œprisonâ€ is mentioned on the â€œlocal newsâ€ pages. At the end of the week, the students report their totals.

The mean result is 40, with a standard deviation of 20.

The distribution of scores is normal. (7 points)

Question: How many students would be expected to count between 50 and 70 cases? (in other words, what proportion of cases fall between 50 and 70 cases â€“ calculate the Z score).

7.  The researcher collapsed the variable income into three categories:   1=Less than \$25,000; 2=\$25,000-50,000; 3= \$50,000-75,000; 4=Greater than \$75,000. What mistake did she make? (2 points)

1. The categories are not mutually exclusive

2. The categories and not exhaustive

3. The variable is interval-ratio and should not have been collapsed

4. The score intervals are not realistic

8.  Tom wants to research the relationship between gender and alcohol. He designs a survey questionnaire, administers it, collects the data, enters the data into SPSS, and conducts ______________________ analysis. (2 points)

1. primary

2. secondary

9. A state department has a policy whereby it accepts as police officers only those who score in the top 5 % of a qualifying exam.

The mean of this test is 50.

Standard deviation is 10.

1. Would a person with a raw score of 85 be accepted? (7 points)

10. Assume you have administered a test to random sample of N-sample=100 workers at your company. The test is purported to have a population standard deviation = 8.0

The test results reveal a sample MEAN=50.   (4 points)

Question: What is the formula to calculate the CI (confidence interval) in this example? â€“ you donâ€™t need to calculate the CI, just show the formula.

11. A sample of 200 (N=200) incidents of mass murder reveals that the mean number of victims per incident is 50, with a standard deviation of 30.

Sample mean=50

S= 30

N=200

Calculate the 85% confidence interval (CI) for number of victims per mass murder incident and interpret your results. (6 points)

12.If a variable has two modes it is called: (2 points)

1. unimodal

2. skewed multimodal

3. bimodal

1. A university professor was interested in identifying left-handed students from all of the six introductory-level psychology classes in the department. The number of left-handed students in each class is: 4, 5, 40, 3, 2, 1. (2 points)

Question: What is the range?

14.What is the mode for the following distribution of scores? (3 points)

## Frequency

Blue

700

Brown

200

Hazel

832

Green

239

15. Assume you have administered a worker satisfaction test to random sample of  N-sample=24 workers at your company. The test is purported to have a population standard deviation = 5

The test results reveal a sample MEAN=60.   (8 points)

Question: Based on the information, develop an estimate of the mean score for the entire population of workers, using a 80% Confidence Interval.

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