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Purpose: This project is to help you apply co

Purpose:

This project 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; and use StatCrunch to carry out the procedures and interpret the output.

Directions:

  • In an article in the Journal of Statistics Education (vol. , no 2), Allen Shoemaker describes a study that was reported in the Journal of American Medical Association (JAMA). It is generally accepted that the mean temperature of an adult human is 98.6°F. In his article, Shoemaker uses the data from the JAMA article to test his hypothesis. The data for the JAMA article were collected from healthy men and women, ages 18 to 40, at the University of Maryland Center for Vaccine Development, Baltimore. [Elementary Statistics: Picturing the World by Ron Larson and Betsy Farber 7th Ed.]
  • Data: Click on “StatCrunch” on MyLab Statistics, then “Data sets from the textbook”. Scroll down to Chapter 7, then click on Chapter 7: Case Study: Human Body Temperature: What’s Normal?

Do all of the work below with the “Women” data set Download “Women” data set.

  • Use a statistical software package to complete the analysis of Exploratory Data Analysis and Inferential Statistics. You are strongly encouraged to use StatCrunch (in MyLab Statistics).  You may also use any other software packages (s.a. MINITAB, or SPSS). However, if you use other software, you are on your own, for your instructor will only help with question with regards to StatCrunch.

A) Exploratory Data Analysis

  1. Construct a stem and leaf display.
  2. Construct a histogram.
  3. Construct a boxplot and use it to investigate the data for outliers.
  4. Obtain the sample mean, median, mode, and standard deviation.

B) Inferential Statistics

  1. Construct a normal probability plot or quantile-quantile (QQ) plot to assess normality. Use this assessment to determine which tests are appropriate for these data for confidence interval and test of hypothesis as you will use these procedures for parts 2 and 3 below.
  2. Construct a 95% confidence interval for µ, for mean body temperature for all adult females in the population.
  3. At the 5% significance level, do the data provide sufficient evidence to conclude that the mean body temperature of women is 98.6°F?
  4. Using the software output, perform the confidence interval and the full hypothesis test.
  • Write a summary and findings of the project

C) Write-up

  • Write a brief introduction of the project.
  • Interpret the mean, and standard deviation in context of the data given.
  • Compare the measures of center and comment on which measure of center would best describe the data given.
  • Comment on the shape of the distribution.
  • Are there any outliers in the data? Include results of your investigation for outliers.
  • Comment on your assessment of normality.
  • Which test will be most appropriate for the inferential statistics? Z-test or t-test? Why?
  • Write an interpretation for the confidence interval estimate in context of the data.
  • State the hypothesis (the null and the alternative)
  • State the conclusion and summary of the significance test and interpret the p-value using the context of the data.
  • Compare the results from the confidence interval and the significance test. Are they the same? Why do think this is the case?
  • Submit your project as an attachment via the link above using the following format in a Microsoft Word or pdf document
    • First page – Title page including your name, course number, and section number
    • Second page – Write – up (See Part C)
    • Final pages – Statistical Software Output and Additional Work (See Parts A and B)

Note:

  1. You must use complete sentences and correct grammar/spelling.
  2. Use StatCrunch to generate tables and graphs for analysis.
  3. Title and Label all of the graphs obtained.

Grading 

This project is worth 100 points.  Please print the rubric Download the rubricfor grading guidelines.

Body Temperature (in degrees F)

Men Women
96.3 96.4
96.7 96.7
96.9 96.8
97 97.2
97.1 97.2
97.1 97.4
97.1 97.6
97.2 97.7
97.3 97.7
97.4 97.8
97.4 97.8
97.4 97.8
97.4 97.9
97.5 97.9
97.5 97.9
97.6 98
97.6 98
97.6 98
97.7 98
97.8 98
97.8 98.1
97.8 98.2
97.8 98.2
97.9 98.2
97.9 98.2
98 98.2
98 98.2
98 98.3
98 98.3
98 98.3
98 98.4
98.1 98.4
98.1 98.4
98.2 98.4
98.2 98.4
98.2 98.5
98.2 98.6
98.3 98.6
98.3 98.6
98.4 98.6
98.4 98.7
98.4 98.7
98.4 98.7
98.5 98.7
98.5 98.7
98.6 98.7
98.6 98.8
98.6 98.8
98.6 98.8
98.6 98.8
98.6 98.8
98.7 98.8
98.7 98.8
98.8 98.9
98.8 99
98.8 99
98.9 99.1
99 99.1
99 99.2
99 99.2
99.1 99.3
99.2 99.4
99.3 99.9
99.4 100
99.5 100.8

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Option 1

MTH 245 DATA ANALYSIS PROJECT (Body Temperature in degrees Farenheit) – 1A and 1B
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 statistical analysis using context of data. – separate points below
Inferential Analysis – Confidence Interval and Full Hypothesis Test (Significance Test) 20
Stated the practical interpretation for the XX% confidence interval within context. 5
Correct null hypothesis 2
Correct alternative hypothesis 2
Correct p-value 2
Correct decision: {Reject H0, Do not reject H0} 2
Correct basis for decision: (comparison of p-value to α) 2
Correct conclusion in context 3
Compared the results of the CI and hypothesis test-matched or not and why? 2
Statistical Package Output 40
Stem and Leaf Diagram (with appropriate title) 4
Histogram 2
* class limits on horizontal axis 2
* appropriately titled graph and titled axes 2
Box and Whiskers Plot (with appropriate title for graph and data axis) 4
used fences to identify outliers 1
Descriptive Statistics 10
* in table form 1
* number of observations 1
* mean 2
* median 2
* mode 2
* sample standard deviation 2
Inferential Techniques 15
QQ Plot (with appropriate tile for graph and data axis) 5
Interval bounds for two-sided CI for µ 5
Results of statistical test of hypothesis 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
* Complete significance test
* Sources/References – if applicable
TOTAL POSSIBLE POINTS 100
COMMENTS:

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