Applied Business Statistics

Project-2

• You can discuss this lab-work with any other student in the class.

• You can get help or clarification from the instructor.

• You are permitted to use the course notes, books, the internet, Rscript posted on blackboard, and any other materials you like.

• For each question, you need to fully interpret your results. Your report should be typed. You should include your code as an appendix and cite your output properly.

• You can upload your lab-work file under lab assignment folder in Blackboard.

• Late submission is not accepted.

• lab-2 data is available under Data folder in Blackboard.

• Use of RStudio is required for all project in this class.

Project Data-Description

Measuring body fat is not simple. Muscle and bone are denser than fat so an estimate of body

density can be used to estimate the proportion of fat in the body. Measuring someone’s weight

is easy but volume is more difficult. One method requires submerging the body underwater in a

tank and measuring the increase in the water level. Most people would prefer not to be submerged

underwater to get a measure of body fat so we would like to have an easier method. In order

to develop such a method, researchers recorded age, weight, height, and 10 body circumference

measurements for 252 men. Each man’s percentage of body fat was accurately estimated by an

underwater weighing technique. We wish to predict body fat using just the easy-to-record mea-

surements.

For simplicity, four variables selected for the study are listed in Table.

Use data: Project-2-data.xls from Blackboard

Variable Description X1 chest circumference (cm) X2 percent body fat using Brozek’s equation X3 weight (lbs) (‘Heavy’ if greater than 180, ‘Light’ otherwise) X4 height (inches) (‘Tall’ if greater than 70, ‘Short’ otherwise)

1. [4 pts] For each variable, describe it as quantitative or qualitative.

2. [8 pts] Develop appropriate descriptive statistics to summarize the data.

3. [6 pts] Draw a histogram for each continuous variable. Interpret.

4. [4 pts] Draw a scatter plot between two continuous variables.

5. [6 pts] Draw a bar graph for each categorical variable.

6. [6 pts] For each continuous variable, compute the 95% confidence interval for a population

mean.

7. [6 pts] For each continuous variable, compute the 95% confidence interval for a population

variance.

8. [6 pts] For each continuous variable, perform a statistical test to see whether its population

mean is zero or not.

9. [10 pts] For each categorical variable, perform a t-test on x2. (that is, test whether there is

significant mean difference on x2 between two levels of each categorical variable)

10. [5 pts] Calculate correlations between continuous variables.

11. [5 pts] Perform a statistical test to see whether the correlation between two continuous variables

is significant or not.

12. [10 pts] Test independence between categorical variables.

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