A blood pressure medication that has been prescribed by doctors has come under
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A blood pressure medication that has been prescribed by doctors has come under

Project: A blood pressure medication that has been prescribed by doctors has come under scrutiny with those who have taken the drug claiming the drug negatively effects their cholesterol and causes weight gain. Some researcher want to know if this medication does indeed leads to cholesterol issues and weight gain, so these researchers conducted a study of 300 subjects who take blood pressure medication and measure the subject's LDL ("bad" cholesterol), HDL ("good" cholesterol), and BMI. The researchers will then compare the study's data with data from the Center for Disease Control and Prevention for cholesterol and BMI. Based on data from 2015-2016, the Center for Disease Control and Prevention reported that 18% of the adult population in the United States had low HDL levels, 33.5% had high LDL levels, and 39.8% were considered obese. 

Data Set:  Statdisk; Essentials of Statistics 6th Edition

Data Set 1: Body Data

For this project, you will analyze data for HDL and LDL cholesterol levels (mg/dL) and BMI - body mass index (kg/m2). Data will be analyzed based the 300 subjects in our sample. The figures below will be used for information regarding the different categories of data to be analyzed. 

Table 1: Desirable Cholesterol Levels

Total cholesterol

Less than 200 mg/dL

LDL ("bad" cholesterol)

Less than 100 mg/dL

HDL ("good" cholesterol)

60 mg/dL or higher

Table 3: CDC Population Percentages

High LDL

33.5%

Low HDL

18%

Obese

39.8% 

Table 2: Standard BMI Categories

Weight Status Category

BMI Range (kg/m2)

Under weight

Below 18.5

Healthy weight

18.5 to 24.9

Over weight

25 to 29.9

Obese

30 or greater

Part A: Comparing the number of subjects to the theoretical expected values

Given the population data in Table 3 we can look at the analysis of the number of subjects with Low HDL, High LDL, and High BMI as a binomial distribution. Remember, the mean and standard deviation of a binomial distribution are as follows: 

1.     Using the proportions in Table 3, determine the mean and standard deviation for HDL, LDL, and BMI based on a sample of 300 adults.

2.     Use the range rule of thumb to identify limits separating values that are significantly low and significantly high.

Open your data for your subjects on Stat Disk

Data Set:  Stat Disk; Essentials of Statistics 6th Edition

Data Set 1: Body Data 

3.     Determine the number of subjects in our sample data that would be considered to have low HDL, high LDL, and according to BMI would be considered obese. 

a.     Based on your results, would the number of subjects in our data set with low HDL be considered significantly low, significantly high, or neither? Justify your reasoning.  

b.     Based on your results, would the number of subjects in our data set with high LDL be considered significantly low, significantly high, or neither? Justify your reasoning.  

c.     Based on your results, would the number of subjects in our data set with a BMI at the obese level be considered significantly low, significantly high, or neither? Justify your reasoning. 

For questions 4 to 8: Use the binomial distribution function on Stat Disk, to answer the following probability questions. Remember, it is important to read the question carefully and determine if the value mentioned should be included in the probability.

•      Identify your sample size, probability of success, and x value inserted into Stat disk.

•      Also, Identify the column and the probability given.

•      Describe what the probability tells us about our data set 

Example: For the probability of less than 40 subjects having low HDL in our sample

Sample size = 300, probability of success = 0.18, x value = 39 (since 40 is not included)

Column = P(x or fewer)    Probability = 0.01226

This probability suggests a 1.2% chance of having less than 40 subjects with low HDL given an 18% of the population is believed to have low HDL. This percentage is significantly low since it is lower than 5% suggesting having less and 40 subjects with low HDL wouldn't occur by chance 

4.     Find the probability of exactly the number of low HDL subjects in data sample.

5.     Find the probability of at least the number of high LDL subjects in data sample. 

6.     Find the probability of less than the number of high LDL subjects in data sample. 

7.     Find the probability of more than our number of obese subjects. 

8.     Find the probability of at most our number of obese subjects. 

9.     What does your analysis tell you about our subjects with respect to low HDL?

10.  What does your analysis tell you about our subjects with respect to high LDL?

11.  What does your analysis tell you about our subjects with respect to high BMI? 

Part B: Analyzing the levels of our data 

1.     Assess HDL, LDL, and BMI data for normality using the normality assessment on Stat Disk. 

a.     Record the following for each category in the table below

i.    Describe the histogram

ii.    How many outliers

iii.    Go to the data set and list the outliers

iv.    If the is at least one "fail to reject result" then list it as a fail to reject normality 

Histogram

Number of Outliers

List all Outliers

Normality

Reject/fail to reject

HDL

LDL 

BMI 

2.     Delete all subjects that are outliers in the data set. That is, their data must be deleted in each category. (Hint: You should delete 20 data points) 

3.     Assess HDL, LDL, and BMI data for normality using the normality assessment on Stat Disk again.

a.     Record the following for each category in the table below

i.    Describe the histogram

ii.    How many outliers

iii.    Go to the data set and list the outliers

iv.    If the is at least one "fail to reject result" then list it as a fail to reject normality 

Histogram

Number of Outliers

List all Outliers

Normality

Reject/fail to reject

HDL

LDL

BMI

4.     Determine the mean and standard deviation of the remaining LDL and BMI data and consider these to be our population parameters.     

In questions 5 to 12 you will want to refer to table 1 for your x value that separates Low LDL and High LDL, that separates an overweight BMI from a obese BMI, and that separates the healthy region.

Examples: If we wanted to know the probability of one individual to be underweight.

Since we are looking at underweight, we will take x value as 18.5,      

Since we are wanting below the 18.5 we will take the area to the left, which is 0.037 or 3.7%

So, based on our data, there is a 3.7% chance of having a BMI that is underweight for one individual.

Examples: If we wanted to know the probability of ten individual to be underweight.

We will need to adjust the standard deviation by dividing by      

Since we are wanting below the 18.5 we will take the area to the left, which is 0.0 or 0%

So, based on our data, there is a 0% chance of having an average BMI that is underweight for ten individuals. 

5.     If one individual is selected at random, determine the probability that they have high LDL cholesterol. (Refer to table l for your x value that separates Low LDL from high LDL) 

6.     If a sample of 300 individuals are randomly selected, determine the probability that their average LDL cholesterol level would be considered high. (Refer to table l for your x value that separates Low LDL from high LDL)

 7.     Describe what each probability means in questions 5 and 6.

8.     If one individual is selected at random, determine the probability that they are considered obese. (Refer to table 3 for your x value that separates Obese from non-obese) 

9.     If a sample of 300 individuals are randomly selected, determine the probability that their average BMI would place them in the obese category. (Refer to table 3 for your x value that separates Obese from non-obese) 

10.  Describe what each probability means in questions 8 and 9. 

11.  If one individual is selected at random, determine the probability that they are considered to be at a healthy weight. (Refer to table 3 for your x value that separates healthy category from non-healthy) 

12.  If a sample of 300 individuals are randomly selected, determine the probability that their average BMI would place them in the healthy weight category. (Refer to table 3 for your x value that separates healthy category from non-healthy) 

13.  Describe what each probability means in questions 11 and 12.


Hint
StatisticsBinomial distribution: It is a probability distribution which summarizes the likelihood that is a value takes one of the two independent values under the given set of assumptions or parameters. Binomial distribution has the underlying assumptions that there is going to be only one outcome for each trial, where each trial contains the same probability of success, and each trial is mutuall...

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