# 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.

**Directions:**

Do all of the work below with the Database of

MATH ACT SCORES

Download 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**

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 Are there any outliers in the data? Include results of your investigation for outliers. Identify which class level has an outlier

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

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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)

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Format

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* 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

COMMENTS:

100

SEX AGE CLASS

F

22 Junior

M

21 Senior

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22 Senior

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21 Sophomore

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22 Senior

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21 Junior

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20 Freshman

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22 Senior

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20 Sophomore

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23 Junior

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20 Sophomore

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22 Senior

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20 Sophomore

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22 Senior

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21 Senior

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22 Senior

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21 Junior

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21 Senior

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19 Sophomore

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19 Sophomore

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20 Freshman

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22 Senior

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23 Senior

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23 Sophomore

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19 Freshman

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22 Senior

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21 Senior

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20 Freshman

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21 Sophomore

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24 Senior

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23 Senior

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19 Sophomore

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19 Sophomore

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18 Freshman

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20 Junior

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22 Senior

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19 Sophomore

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20 Sophomore

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21 Senior

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27 Senior

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19 Sophomore

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20 Sophomore

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19 Sophomore

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21 Senior

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20 Freshman

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21 Senior

MATH

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Sophomore

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24

Freshman

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