# MTH 245 NVCC Statistical Techniques Paper

Purpose:

### Thisproject is to help you apply concepts to real world, real data analysis. In the real-world computers do most of the hard work for statisticians.  This project will help you understand how an informative decision is made using data analysis.  After completing this project, you should be able to determine which statistical procedures are appropriate; use StatCrunch to carry out the procedures and interpret the output

The Database of UVA (Excel file) students contains information on the undergraduate students at University of Virginia. This list contains the data for different Qualitative and Quantitative variable. Your project is to obtain the results based on the following questions using StatCrunch. Copy the StatCrunch results (graph plus answer) into summary document using the guidelines in section C.

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Directions:

Do all of the work below with the Database of

MATH ACT SCORES

### Data: The Data set is on the project page on canvas(MATH ACT SCORES). Use StatCrunch (in MyLab Statistics) to obtain results for the following questions.

A) Exploratory Data Analysis

Obtain the mean and standard deviation for ACT Math scores for each class level (freshmen, sophomores, juniors, seniors) and interpret the results

Obtain the five number summary of ACT Math score for each class levels. Do any of these class levels have outliers?

Construct a boxplot and use it to investigate the data for outliers

Construct a histogram, and normal probability plot (QQ Plot) for ACT Math score for each class level,

B) Inferential Statistics

6. Construct and interpret a 95% confidence interval for µ, for the mean ACT Math score for each class level.

7 Using regression analysis (hint, use scatter plot, r, r2 ) , investigate if there is a relationship between Age and performance in ACT Math score.; . provide an equation can be used to predict ACT math score based on age,

Write a Summary and Findings of the Project

C) Write-up

• Write a brief introduction of the project.
• o             Interpret the mean, and standard deviation in context of the data given.

o             Compare the measures of center and comment on which measure of center would best describe the data given.

• o             Comment on the shape of the distribution, which class level appears to be more approximately normal
• o             Are there any outliers in the data? Include results of your investigation for outliers. Identify which class level                 has an outlier

• o             Comment on your assessment of normality.
• o             Which test will be most appropriate for the inferential statistics (confidence Interval)? Z-test or t-test? Why?
• o             Write an interpretation for the confidence interval estimate in context of the data.
• o             State the summary, interpretation and conclusion of your Investigation if there is a relationship between                     Age and performance in ACT Math score of undergraduate student at UVA.; Provide an equation can be used               to  predict ACT math score based on age; how reliable would  the prediction be?
• MTH 245 DATA ANALYSIS PROJECT (UVA ACT MATH SCORES)
Written Summary
35
The student demonstrates an understanding of key concepts and adequately address all aspects
of this analysis assignment. The assignment report is submitted as a formal paper in paragraph
form and is well written with full sentences, and is typed and well formatted with appropriate
grammar, spelling, and punctuation.
* Brief introductory paragraph regarding the background of data.
* Specified the shape of the distribution of the data and referenced graph(s) used to make
decision.
* Discussed the presence or absence of outliers.
* Discussed which measure of center was most appropriate (the values of mean, median, and
mode) within context.
* Interpreted the mean and standard deviation in context of the data.
*commented on the assessment of normality (QQ plot)
*Commented on which test to use and why (z-test or t-test)
Interpret results of regression analysis using context of data. – separate points below
Inferential Analysis – Confidence Interval and Regression Analysis
Stated the practical interpretation for the XX% confidence interval within context.
Correct r (correlation coefficient)
Correct r2 (coefficient of determination)
Scatter plot
Correct interpretation of r
correct interpretation of r2 (Cofficient of determination)
Correct conclusion in context if a relationship exist between Age and Math ACT scores
correct regression equation
Statistical Package Output
QQ plot (with appropriate title) for each class level
Histogram( for each of the class level)
* correct identification of which class level is more normally distributed.
* appropriately titled graph and titled axes
Box Plot (with appropriate title for graph and data axis) for each class level
used fences to identify outliers
Descriptive Statistics
* in table form
* number of observations
* mean
* median
* IQR
*quartiles
Inferential Techniques
5
5
5
5
4
3
8
20
5
2
2
2
2
2
3
2
40
4
4
2
2
4
2
12
1
1
2
2
2
4
10
Correct interpretation of confidence interval for each class level
Confidence interval for each class level
Results of Regression analysis (if there is a relationship or not)
5
5
Format
5
* Title page with appropriate title, name, course number and section number
* Summary
* Statistical software output for graphical summaries
* Statistical software output for numerical summaries
* Statistical software output for inferential techniques
* Statistical software output for regression analysis
* Sources/References – if applicable
TOTAL POSSIBLE POINTS
100
SEX AGE CLASS
F
22 Junior
M
21 Senior
F
22 Senior
M
21 Sophomore
M
22 Senior
M
21 Junior
F
20 Freshman
F
22 Senior
M
20 Sophomore
F
23 Junior
F
20 Sophomore
F
22 Senior
M
20 Sophomore
F
22 Senior
F
21 Senior
F
22 Senior
F
21 Junior
M
21 Senior
F
19 Sophomore
M
19 Sophomore
F
20 Freshman
M
22 Senior
M
23 Senior
F
23 Sophomore
M
19 Freshman
M
22 Senior
M
21 Senior
F
20 Freshman
F
21 Sophomore
F
24 Senior
M
23 Senior
F
19 Sophomore
M
19 Sophomore
M
18 Freshman
F
20 Junior
M
22 Senior
M
19 Sophomore
F
20 Sophomore
M
21 Senior
F
27 Senior
M
19 Sophomore
F
20 Sophomore
F
19 Sophomore
F
21 Senior
M
20 Freshman
F
21 Senior
MATH
28
23
25
19
28
26
14
23
18
22
23
26
24
24
18
27
20
25
21
26
22
28
28
25
18
25
28
21
26
18
21
20
30
25
25
25
25
20
32
18
21
28
27
27
25
22
F
M
F
F
M
F
M
M
M
F
M
M
F
F
F
M
F
M
M
M
M
M
F
M
F
F
M
F
M
F
M
F
F
F
F
M
F
M
F
M
F
F
F
M
M
F
F
19
21
21
21
20
23
20
21
22
20
21
19
21
20
22
20
22
20
23
20
22
22
21
18
22
19
21
18
20
21
19
21
19
19
20
19
20
22
21
19
18
21
21
20
18
20
19
Sophomore
Junior
Senior
Junior
Junior
Senior
Sophomore
Sophomore
Senior
Junior
Junior
Freshman
Senior
Junior
Junior
Sophomore
Junior
Freshman
Senior
Junior
Senior
Junior
Sophomore
Freshman
Junior
Freshman
Junior
Freshman
Sophomore
Junior
Freshman
Senior
Sophomore
Sophomore
Junior
Freshman
Junior
Senior
Senior
Freshman
Freshman
Sophomore
Senior
Sophomore
Freshman
Junior
Sophomore
26
17
21
19
23
25
19
27
21
19
23
26
21
24
16
22
21
25
24
23
27
18
18
30
24
24
30
21
20
22
23
24
20
19
21
31
23
26
20
19
26
21
21
27
26
26
26
F
M
F
M
M
M
F
M
F
M
F
F
F
F
F
F
F
F
F
F
M
M
F
F
F
F
F
M
M
M
F
M
M
M
M
F
M
M
M
F
M
M
F
F
F
M
F
20
20
19
23
21
19
19
22
22
22
21
19
22
22
20
18
21
22
18
20
22
24
21
19
20
21
21
20
22
20
21
20
35
20
21
19
22
21
21
19
22
20
22
22
19
20
23
Junior
Sophomore
Sophomore
Senior
Junior
Sophomore
Sophomore
Senior
Senior
Senior
Sophomore
Freshman
Senior
Senior
Sophomore
Freshman
Senior
Senior
Freshman
Sophomore
Junior
Senior
Junior
Sophomore
Junior
Junior
Junior
Sophomore
Senior
Sophomore
Senior
Sophomore
Senior
Sophomore
Senior
Freshman
Senior
Junior
Junior
Sophomore
Senior
Sophomore
Senior
Junior
Freshman
Junior
Senior
25
24
23
24
25
30
25
27
26
26
21
20
25
30
22
24
22
23
20
21
20
24
19
21
23
20
18
24
31
21
24
15
28
22
29
24
21
26
27
26
22
28
19
28
22
28
23
F
M
M
M
F
M
F
F
F
F
F
M
M
F
M
F
F
M
F
F
M
M
F
F
F
F
F
F
F
F
F
F
F
F
F
F
M
F
F
F
F
M
F
M
M
M
M
19
22
21
22
20
21
20
21
18
23
20
23
22
20
22
20
19
23
21
19
20
21
18
20
20
20
19
19
20
20
20
21
21
22
35
22
22
20
19
20
22
21
22
20
20
22
24
Freshman
Senior
Sophomore
Senior
Sophomore
Senior
Junior
Junior
Sophomore
Senior
Sophomore
Senior
Junior
Sophomore
Senior
Junior
Sophomore
Senior
Junior
Sophomore
Junior
Junior
Freshman
Junior
Sophomore
Junior
Sophomore
Sophomore
Sophomore
Sophomore
Sophomore
Junior
Senior
Senior
Junior
Senior
Junior
Junior
Freshman
Junior
Junior
Senior
Junior
Junior
Sophomore
Senior
Senior
18
29
17
25
23
20
17
26
25
24
26
27
24
21
24
30
32
23
34
25
26
26
27
26
17
30
16
26
17
23
18
29
23
21
17
27
27
28
23
29
15
25
23
31
19
27
20
M
M
F
F
F
F
F
F
F
F
F
F
F
22
19
21
19
22
32
21
18
20
21
20
22
20
Senior
Sophomore
Junior
Sophomore
Junior
Senior
Junior
Freshman
Sophomore
Junior
Sophomore
Senior
Sophomore
19
29
19
26
24
26
32
24
18
19
29
21
20

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