SAT Performance
This is the first of two related Tasks. In these Tasks you will investigate four questions about students' SAT scores at one high school.
1. What is the mean SAT-Math score at this high school?
2. How do these students' SAT Math scores stack up against the rest of the state?
3. Is there a significant difference between Verbal and Math scores for these students?
4. Nationally males tend to have higher Math scores than females. Is that true at this high school, too?
You have a copy of data from the SAT Score Roster sent to the high school by the College Board. It shows gender, Verbal scores, and Math scores, for 303 students in a recent graduating class.
NOTE: You will trot use all of these data, just a sample of 20 - 30 students.
Your current assignment: investigate the first two questions posed above.
- Draw a sample of these students, carefully explaining your procedure.
- Use your sample to create a 95% confidence interval for the mean SAT-I Math score at this high school.
- Based on your confidence interval, compare the performance of these students with the statewide mean Math score of 503.
- Prepare a written report that includes complete demonstrations of the statistical procedures you use and your conclusions (in context, of course).
SAT Performance (Part II)
In this Task you will continue your investigation of the four questions we posed about one high school's SAT scores
1. What is the mean SAT-Math score at this high school?
2. How do these students' SAT Math scores stack up against the rest of the state'!
3. Is there a significant difference between Verbal and Math scores for these students?
4. Nationally males tend to have higher Math scores than females. Is that true at this high school, too?
You should still have your copy of data from the SAT Score Roster sent to the high school by the College Board. It shows gender, Verbal scores, and Math scores, for 303 students in a recent graduating class.
Again you will not use all of these data, just a sample of 20 - 30 students.
Your new assignment: investigate the last two questions posed above.
- Use a sample of these students. It may be the same sample you used previously, or you may draw a new one, carefully explaining your procedure.
- Determine whether your sample provides statistical evidence that Verbal and Math scores differ for students at this high school.
- Determine whether your sample provides statistical evidence that males have higher Math scores than females at this school.
- Prepare a written report that includes complete demonstrations of the statistical procedures you used and your conclusions (in context, of course).
97 AP Stat Scores
1997 was the first year for Advanced Placement Statistics nationwide. How well did Ithaca High School students do on the AP exam? Here are the summary statistics reported by the College Board for that year's AP Statistics and BC Calculus exams, as well as a breakdown of the AP Stat scores by gender.
|
AP Stat Grade
|
Grade Distributions
|
|
Global
|
Group
|
|
5
|
15.60%
|
49.0%
|
|
4
|
22.1%
|
30.6%
|
|
3
|
24.5%
|
16.5%
|
|
2
|
19.6%
|
4.4%
|
|
1
|
18.1%
|
0.0%
|
|
Candidates
|
|
49
|
|
AP Grade
|
Calculus BC
|
Statistics
|
|
5
|
29
|
24
|
|
4
|
8
|
15
|
|
3
|
6
|
8
|
|
2
|
1
|
2
|
|
1
|
|
|
|
Total
|
44
|
49
|
|
AP Stat Grade
|
Gender
|
|
M
|
F
|
|
5
|
19
|
5
|
|
4
|
8
|
7
|
|
3
|
5
|
3
|
|
2
|
1
|
1
|
|
1
|
0
|
0
|
Some questions to consider:
1. How did IRS AP Stat scores compare to the national results?
2. How did AP Stat students do compared to the BC Cale students?
3. DO these results indicate that IRS males and females may perform differently on the AP Statistics exam?
Write a report assessing the success of this first group of AP Statistics students with respect to the questions above. Indicate the hypotheses you test and the types of tests you do (goodness of fit, homogeneity, independence), show appropriate calculations and results, and clearly state your conclusions.
Statistics Quiz
The EPA is examining the relationship between the ozone level (in ppm) and the Population (in millions) if US cities. Part of the regression is shown below.
R2 = 84.4%
s = 0.0809 with 35 degrees of freedom
variable coefficient SE(coeff.)
intercept 18.892 2.395
population 6.650 1.910
1) Is the relationship between population and high ozone level significant? Assume the conditions for inference are satisfied. State an appropriate hypothesis, test it, and state your conclusion in context.
2) Do you think that the population of a city is a useful predictor of ozone level? Use the values of R2 and s in your explanation.
3) Use your model to construct a 95% confidence interval for the ozone level in a city whose population is 12.4 million.
4) Below are the speeds of several models of printer (pages per minute), and the cost of printing with them (in cents/page). Is there evidence of an association between speed and cost? State and test an appropriate hypothesis and state your conclusion.
|
Speed
|
Cost
|
|
4.6
|
12.0
|
|
5.5
|
8.5
|
|
4.5
|
6.2
|
|
3.8
|
3.4
|
|
4.6
|
2.6
|
|
3.7
|
4.0
|
|
4.7
|
5.8
|
|
4.7
|
8.1
|
|
4.0
|
9.4
|
|
3.1
|
14.9
|
|
1.9
|
2.6
|
|
2.2
|
4.3
|
|
1.8
|
4.6
|
|
2.0
|
14.8
|
|
2.0
|
4.4
|
Attachment:- SAT Performance Data.rar