Every two years, the Centers for Disease Control and Prevention conduct the Youth Risk Behavior Surveillance System (YRBSS) survey, where it takes data from high schoolers (9th through 12th grade), to analyze health patterns. You will work with a selected group of variables from a random sample of observations during one of the years the YRBSS was conducted.
Load the yrbss data set, which can be found here into your
workspace.
There are observations on 13 different variables, some categorical and some numerical. The meaning of each variable can be found by visiting this page.
You will first start with analyzing the weight of the participants in
kilograms: weight.
Using visualization and summary statistics, describe the distribution of weights.
weight? Make a
historgram or boxplot of weight. Describe the distribution
of weights (shape, center, and spread).Next, consider the possible relationship between a high schooler’s weight and whether they strength train. Plotting the data is a useful first step because it helps us quickly visualize trends, identify strong associations, and develop research questions.
Note: the problem has been changed to reflect the new definition that student strength trains if they do strength training more than 1 day a week
First, let’s create a new computed variable strength,
which will be coded as either “yes” if the student does strength
training more than 1 day a week. Type or click the following
function:
IF(strength_training_7d>1,"yes","no").
Double check the first three observations to confirm that the variable is correct.
weight split by
strength. Describe the distributions (shape, center, and
spread), using descriptive statistics if necessary. Do you see a
difference between the two distributions?There is an observed difference, but is this difference large enough to deem it “statistically significant”? In order to answer this question we will conduct a hypothesis test. we want to test whether the mean weights are different for high school students who strength train and those who don’t.
What are the parameters of interest? What are the hypotheses?
Are all conditions necessary for inference satisfied? Explain in detail, and include descriptives or plots in your justification.
Perform an independent samples t-test.
We will now confirm that this p-value is the same if we compute the probablility directly.
Open the distrACTION menu (click the plus sign and check
the box if you don’t see the menu at the top), and select
T Distribution. Enter the degrees of freedom from Exercise
5 in df, and leave \(\lambda\) as
0.
In the options, click to highlight Compute probability,
then replace \(x_1\) with the
t-statistic from Exercise 5. This is the critical t-value for our
sample. Choose the appropriate option for the probability (either \(P(X \leq x_1)\) or \(P(X \geq x_1)\)), depending on your
t-statistic. You will see a probability value show up, and the area will
be highlighted.
Compare p-value from the Independent Samples Test, and the probability from the distrACTION T Distribution. Include the output from the distrACTION module. What does the p-value represent?
What conclusion can you make based on the p-value?
Is your conclusion valid (your answer should be based on Exercise 4)? Explain briefly.