Overview - Confidence Intervals for the Mean Height of American Adults The National Health and Nutritional Examination Survey (NHANES) is a population survey implemented by the Centers for Disease Control and Prevention (CDC). Although NHANES encompasses tens of thousands of individuals and 1,191 variables, we will look at height measurements of 18,391 individuals older than 19 years of age. The purpose of this assignment is to estimate 95% confidence intervals for the average height of adults in the NHANES study. Although the NHANES data is a sample of all adults in America, we will pretend that the individuals in the NHANES study comprise the population of interest, and then we will randomly select 10 individuals from the NHANES data to construct 95% confidence intervals for the mean height of the NHANES population. Since we have the benefit of ascertaining the mean height of the NHANES population, we can observe whether our confidence intervals actually contain the population mean. Learning Outcomes 1. Calculate and interpret measures of the location of data: quartiles, percentiles, and z-scores (CLO: A). 2. Calculate and interpret measures of the center of data: mean, median, and mode (CLO: A). 3. Calculate and interpret measures of the variability of data: variance, standard deviation, and range (CLO: A). 4. Construct confidence intervals for a population mean (CLO: A, B, C). 5. Interpret confidence intervals for a population mean (CLO: A, B, C). 6. Find the probabilities of normal random variables using R functions (CLO: B, D). 7. Find quantiles and percentiles of normal random variables using R functions (CLO: B, D). 8. Find the probabilities of T random variables using R functions (CLO: B, D). 9. Find quantiles and percentiles of T random variables using R functions (CLO: B, D). Directions 1. Find the mean and standard deviation of the height measurements for all the individuals in the NHANES population. 2. Randomly select 10 individuals from the NHANES data and report the sample values in a table. 3. Report the five-number summary, mean, and standard deviation of your sample within a table. 4. Calculate a 95% Confidence interval for the average height of adults in the NHANES study using the population standard deviation. 5. Calculate a 95% Confidence interval for the average height of adults in the NHANES study using the sample standard deviation. Load the NHANES Data into RStudio · Download this .csv of height data into some folder on your computer. Start RStudio · Select the working directory. The working directory is where RStudio saves and loads files. To select the working directory, follow these steps: 1. 1. Select the "Files" tab next to the console in RStudio. 2. On the "Files" tab, navigate to the folder where you saved the .csv file. 3. Select the "More" menu item. 4. Select "Set as working directory" . Load the .csv file into a data frame by typing the following command into the console. population.dataframe = read.csv("NHANES_project_data.csv") · Assign the height measurements to a vector. population.height = population.dataframe$height Find the Mean and Standard Deviation of the Height Measurements of the NHANES Population Fill in the Blank : Each correct answer earns 2 points (4 points total) Using the Rich Content Editor, report the mean and standard deviation of the height measurements of the NHANES population. Remember that the heights are measured in centimeters. · population mean = < your answer here> · population standard deviation = < your answer here> Randomly Select 10 Height Measurements from the NHANES Population (Fill in the Blank) Fill in the blank : A complete table earns 2 points total. Use the Rich Content Editor to construct a table that lists the height measurements in your sample. You can use the following table as a template. A Sample of Height Measurements X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 <Value><Value><Value> <Value> <Value> <Value> <Value> <Value> <Value><Value> · To assign the number of individuals in the NHANES data to a variable, use the following R code: population.size = length(population.height) · To randomly select 10 height measurements from the population, use the following R code: sample.height = population.height[sample(population.size, 10)] Report the Five-Number Summary, Mean, and Standard Deviation of the Sample (Fill in the Blank) Fill in the Blank : Each correct answer earns 1 point (7 points total) Use the Rich Content Editor to construct a table to hold the five-number summary, sample mean, and sample standard deviation of the height measurements in your sample. Five-Number Summary of the Sample Heights Minimum First Quartile Median Third Quartile Maximum Mean Standard Dev. <your answer here> <your answer here> <your answer here> <your answer here> <your answer here> <your answer here> <your answer here> Calculate a 95% Confidence Interval for the Population Mean Using the Population Standard Deviation (Fill in the Blank) Fill in the Blank : Each correct answer earns 2 points (4 points total) State the lower bound and the upper bound of a 95% confidence interval for the average adult height in centimeters. Please use the population standard deviation to calculate the upper and lower bounds, and show your calculations. Does the interval contain the population mean? Lower Boundary : < your work here> Upper Boundary : < your work here> Calculate a 95% Confidence Interval for the Population Mean Using the Sample Standard Deviation (Fill in the Blank) Fill in the Blank : Each correct answer earns 2 points (4 points total) State the lower bound and the upper bound of a 95% confidence interval for the average adult height in centimeters. Please use the sample standard deviation to calculate the upper and lower bounds, and show your calculations. Does the interval contain the population mean? Lower Boundary : < your work here> Upper Boundary : < your work here>