Overview
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Blood pressure is the pressure that the blood exerts against the walls of the arteries. When physicians or nurses measure your blood pressure, they take two readings. The systolic blood pressure is the pressure when the heart is contracting and therefore pumping. The diastolic blood pressure is the pressure in the arteries when the heart is relaxing. The diastolic blood pressure is always the lower of the two readings. Blood pressure varies from one person to another. It will also vary for a single individual from day to day and even within a given day.
If your blood pressure is too high, it can lead to a stroke or a heart attack. If it is too low, blood will not get to your hands and feet, and you may feel dizzy. Low blood pressure is usually not serious.
So, what should your blood pressure be? A systolic blood pressure of 120 would be considered normal. One of 150 would be high. But since blood pressure varies with gender and increases with age, a better gauge of the relative standing of your blood pressure would be obtained by comparing it with the population of blood pressures of all persons of your gender and age in the United States. Of course, we cannot supply you with that data set, but we can show you a very large sample selected from it. The blood pressure data on persons between the ages of 15 and 20 are provided for you in the data set “Blood_Pressure.” The data are part of a health survey conducted by the National Institutes of Health (NIH). Entries for each person include that person’s age and systolic and diastolic blood pressures at the time the blood pressure was recorded. Use RStudio respond to the following questions. (Source of case study: Mendenhall, Beaver & Beaver, 2015)
- What are the variables that have been measured in this survey? Are the variables quantitative or qualitative? Discrete or continuous? Are the data univariate, bivariate, or multivariate? Explain your responses.
- Construct a relative frequency histogram of the systolic blood pressure data for the males and another for the female. Please use Assignment 4 R Codes located in the R Codes folder on Canvas. You will need to filter the data for the subsets (males and females, lines 23 and 37 respectively).
- Create three Sampling Distributions of 100 samples each with sample size n = 5, n = 50, and n = 100 of the systolic blood pressures in the Blood_Pressure data set. What are the means and standard errors (SE) of each Sampling Distribution?
- Using the sampling distribution with n=50 from problem 3 above, choose the mean of one of the samples in the Sampling Distribution to calculate the confidence interval at the 98% confidence level in problem 5 below. (In class, we looked at a 95% confidence level). To choose one of the means, you can click on the one_hundred_samples_size50 dataset in the global environment pane and view the dataset in the source pane.
- What is the Point Estimate?
- What is the Standard Error?
- What is the Critical Value? (Please use the table provided on Slide 38 of the Class 4 PowerPoint slides in the Canvas file folder)
- Calculate the Confidence Interval using the information you provided in problem 4 above. I am not looking for right or wrong answers. Rather I'm looking for your process. Write a concluding statement about the confidence interval in regards to the population mean.