Statistics - Normal Probability Projects

Unit 1 Homework: Summarizing and Describing Data This homework requires both SPSS and your calculator.

Unit 1 Homework: Summarizing and Describing Data

This homework requires both SPSS and your calculator. There are very specific and helpful guidelines for doing this type of homework located in the Graphing Tutorial in Unit 1. S ubmit only one file for the entire homework into the gradebook . Either create text boxes in SPSS and type in your explanations and answers there, OR, do your work in Word, and cut and paste graphs and tables from SPSS into that document. APA format is required for figure and table captions.

In SPSS, create a database from the information in Table 1 (pg. 3) found at the end of this document. Use that information to answer questions 1 through3.

For the variable Math 201 :
1. Create the appropriate graph (5 pts)
2. Create the appropriate descriptive statistics (5 pts)
3. What is the most appropriate descriptive statistic? Include the justification for your choices (5 pts)
4. Write out how you would explain this information to someone who had not had a course in statistics (5 pts).
For the variable Math Test :
1. Create the appropriate graph (5 pts)
2. Create the appropriate descriptive statistics (2.5 pts)
3. What is the most appropriate descriptive statistic? Include your justification for your choices. (2.5)
4. We know from experience that scores in the middle 50% of the distribution generally do well in our course in statistics. What scores would be the cutoffs for this range? (5 pts.)
  e. Students who score below the 30 ^th percentile on this test are referred to the Tutoring Center. How many should be referred?
  (5 pts.)
For the variable Stat grade :
1. Create the appropriate graph (5 pts)
2. Create the appropriate descriptive statistics (2.5 pts)
3. What is the most appropriate descriptive statistic? Provide justification for your choices. (2.5)
4. What is the probability of finding a score of 90 or better? (5 pts.)
5. What scores mark the most deviant 10%? (5 pts.)
  4. Reading readiness of preschoolers from an impoverished neighborhood (n = 20) was measured using a standardized test. Nationally, the mean on this test for preschoolers is 30.9, with s = 2.08.
  1. Children below the 30 ^th percentile are in need of special assistance prior to attending school. What score would indicate these children? (5 pts.)

b. What percentage of children score between 25 and 28.5? (5 pts.)

c. How many children would we expect to find with scores between 28 and 31.5? (5 pts.)

d. Children in the top 25% are considered accelerated readers and qualify for different placement in school. What score would mark the cutoff for such placement? (5 pts.)

5. Age at onset of dementia was determined for a sample of adults between the ages of 60 and 75. For 15 subjects, the results were $\sum{{{x}_{i}}}=1008$, and $\sum{x_{i}^{2}}=67,878$. Use this information to answer the following:

a. What is the mean and s for this data? (5 pts.)

b. What is the percentile rank for an individual who shows dementia at age 62? (5 pts)

c. If we consider +/-1z to be the normal range of onset, what ages correspond to this? (5 pts.)

d. What ages identify the most deviant 20%? (5 pts.)

Table 1.

Student Database

ID #	Gender	GPA	Math 201	Math Test	Stat Grade
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25	Male Male Female Female Female Male Female Female Female Female Male Male Female Female Female Female Female Female Male Female Female Female Male Male Female	3.23 3.10 3.75 2.32 2.79 2.13 2.64 2.91 2.27 2.53 3.32 3.73 3.24 3.01 2.94 2.80 2.55 3.23 2.94 3.79 3.65 2.15 3.44 2.26 2.95	No Yes Yes No No No No No Yes No Yes Yes Yes Yes No No No No No Yes Yes No No No No	17 27 35 25 28 18 15 29 38 17 35 32 28 22 18 25 24 40 28 38 35 20 36 27 29	78 85 93 74 76 62 58 78 90 60 93 94 90 79 74 72 70 78 73 94 93 62 68 60 60