Question 1: The data from your...
The data from your sample of 80 employees can be found on the tab labelled "Health Exam Results Data." The fasting total cholesterol measurement (mg/dL) is recorded as "cholesterol". Levels below 200 mg/DL are considered normal, levels between 200 and 240 (inclusive) are considered above normal/moderate risk, and levels above 240 are considered high risk. In addition to this variable, there are four more variables in this data set: "sex" which can have a value of either "female" or "male"; "age (years)"; "height (inches)"; and "weight (lbs)". The first step to this analysis is to generate some descriptive measures.
For each of the following points, create the chart and/or graph that best displays the data:
a) Show the breakdown of your sample by gender
b) Show the distribution of cholesterol across all participants.
c) Show the distribution of weight across all participants
Additionally, you want to generate some tables of summary statistics.
d) Create one table that calculates summary measures of cholesterol and weight across all 80 participants.
e) Create a second table that calculates summary measures of cholesterol and weight broken out by gender.
Based on the graphs and tables created in parts a-e:
f) What preliminary conclusions can you draw regarding the differences in cholesterol between male and female employees of this company?
3. Five years ago, this company adminstered the same basic health exam to its employees. At that time, it was found that the mean cholesterol level of the employees was 274.15. This is too high according to health guidelines. You have been asked to determine if the cholersterol level of the employees has changed since the exam that was administered 5 years ago.
a. State your null and alternative hypotheses.
b. Conduct a test of the hypothesis that the mean cholesterol level has not changed since the health exam given 5 years ago.
c. Based on your analysis, what conclusion can we draw about the cholesterol level of the current empoyees?
d. If the goal of the company's wellness program is to reduce the cholesterol levels of its emplyees, should the company add a component to their wellness program that will educate employees about ways they can lower their cholesterol?
2. A healthy cholesterol level is <200. The company wants no more than 25% of its employees to have cholesterol levels that exceed 200.
a. Construct a 95% confidence interval for the proportion of employees who have cholesterol levels higher than 200.
b. Interpret your findings with respect to the company's 25% target.
4. One manager has conjectured that the men have bad dietary habits and probably have high cholesterol readings, which should be the focus of the wellness program. We would like to test the hypothesis that male cholesterol readings are different from female cholesterol readings.
a) Conduct an ANOVA to evaluate whether or not there is a significant difference in cholesterol readings between males and females.
b) Summarize and interpret the results of your test.
5.One manager suggests that the company may be able to check on the progress of the wellness campaign by observing changes in the body mass index instead of redoing the more costly cholesterol reading. There is also some discussion that changes in the BMI may be more effective in reducing male cholesterol readings than female cholesterol readings.The body-mass index is defined as the ratio of the weight to the square of the height, multiplied by 703 if the height is measured in inches and the weight is measure in pounds. BMI = 703*Weight/(Height^2).
a) Create the BMI variable and a dummy variable for sex, called Male, which is zero for females and 1 for males.
b) Estimate a multiple regression model that includes the sex dummy, BMI and an interaction variable between BMI and sex, as independent variables.
c) Calculate predicted values for cholesterol readings for both men and women at BMI values of 20, 25 and 30.
d) Summarize and interpret the results of this model. Is BMI relevant for the program? How do you know? What do you tell the management team about the relative importance of BMI for men and women?
6. Shortly after you publish your findings in a report, you receive a call from a small manufacturing company in Mississippi. The company employs 250 workers in a rural area. They too have investigated their employees' cholesterol levels. However, they are confused because their statistical findings showed nothing significant. What do you tell them and why?
7. The variable the company is most interested in understanding/explaining is cholesterol. You were also given variables that indicated the gender, age, height, and weight of the study participants. If this were a real research project, you would surely collect other data to use as control variables. a) For each of the following variables, explain why you would, or would not, want to collect the data to use in your analysis: 1) normal dietary habits, 2) use of cholesterol lowering medications, 3) music preference, 4) smoking habits, and 5) brand of car owned. b) Name at least one other variable that you would include as a control variable and tell why you would include it.
A few weeks after you finish your report, your boss knocks on your door. She is very concerned about the data and says "the distribution looks a little off to me. Based on data from the Framingham Heart Study, the 99% confidence interval for total cholesterol in the US is approximately 150-350. Single digit total cholesterol is not compatible with life and total cholesterol over 1000 is usually only seen in people with genetic disorders. Your data is very troubling. Can you investigate further to see what is going on?"
Tell me (a) what you would do next (and WHY!!!), and (b) what lessons you might take away from this?
Will Provide data ....