You are to show your work in solving these problems. You can use symbols, R code, or written description. The problems can be written out by hand, or you may use a text editor like MS-WORD. Your solutions should be numbered.
Please answer the following questions.
1) The National Heart, Lung, and Blood Institute defines the following categories based on Systolic Blood Pressure (SBP):
Normal: SBP ? 120.
Prehypertension: 120 < SBP ? 140. High blood pressure: SBP > 140.
From prior experience, it is known that SBP in the United States follows a normal distribution with a mean MU=125 and standard deviation SIGMA= SQRT(152)=12.323. In symbols: SBP ? N(125, 152).
a) Suppose a random sample of n=9 US citizens is obtained and their SBP measured. The sample mean for SBP from this 9 individuals turns out to be: 115. Write down the sampling distribution for this sample mean and find its (ie the sampling distributions) standard deviation.
b) Suppose you want to construct an 80% Confidence Interval on the sample mean of SBP. What is the critical value you would use in the CI computation?
c) What is the margin of error for an 80% Confidence Interval on the sample mean of SBP?
d) Construct and report the 80% Confidence Interval on the sample mean of SBP. How do you interpret this interval?
e) Construct and report a 95% Confidence Interval on the sample mean of SBP. How does this result compare and contrast with that of the 80% Confidence Interval?
f) Suppose a random sample of n=109 US citizens is obtained and their SBP measured. Amazingly, the sample mean of SBP for the n=109 sample is also 115. How do the 80% and 95% confidence intervals compare to those which were done previously?
2.) The trouble with assuming that the Body Mass Index (BMI) in United States follows a Normal Distri
bution with mean 27 and standard deviation of SQRT(62)=7.87, is that assumptions are often just flat out wrong! In other words, suppose we simply do not know the distribution of BMI. Still, we can follow the recommendation by National Heart, Lung, and Blood Institute, we define the following BMI categories:
Underweight: BMI ? 18.5.
Normal weight: 18.5 < BMI ? 25. Overweight: 25 < BMI ? 30. Obesity: BMI > 30.
a) Suppose a random sample of n=9 US citizens is obtained and their BMI measured. The sample mean for BMI from this 9 individuals turns out to be 27, while the sample standard deviation for BMI is 7.68. Write down the sampling distribution for this sample mean of BMI and find its (i.e. the sampling distributions) standard deviation.
b) Suppose you want to construct an 80% Confidence Interval on the sample mean of BMI. What is the critical value you would use in the CI computation?
c) What is the margin of error for an 80% Confidence Interval on the sample mean of BMI?
d) Construct and report the 80% Confidence Interval on the sample mean of BMI. How do you interpret this interval?
e) Construct and report a 95% Confidence Interval on the sample mean of BMI. How does this result compare and contrast with that of the 80% Confidence Interval?
f) Suppose a random sample of n=121 US citizens is obtained and their SBP measured. Amazingly, the sample mean of BMI for the n=121 sample is also 27 with a sample standard deviation of BMI being 7.68 as well. How do the 80% and 95% confidence intervals compare to those which were done previously?
Congratulations! Youve completed Assignment 4. Please save your R-code, because you can re-use or cannibalize this code in future assignments.
Your write-up should address each question. You should label each answer by question number