Task Background: In this week’s discussion, you
learned how to construct probability distributions and graph them. This
week, you will review continuous probabilities, more specifically normal
You are hired as a statistical analyst for Silver’s Gym, and your
boss wants to examine the relationship between body fat and weight in
men who attend the gym. After compiling the data for weight and body fat
of 252 men who attend Silver’s Gym, you find it relevant to examine the
statistical measures and to perform hypothesis tests and regression
analysis to help make general conclusions for body fat and weight in
Part I: Statistical Measures
Statistics is a very powerful topic that is used on a daily basis in
many situations. For example, you may be interested in the age of the
men who attend Silver’s Gym. You could not assume that all men are the
same age. Thus, it would be an inaccurate measure to state that "the
average age of men who attend Silver’s Gym is the same age as me."
Averages are only one type of statistical measurements that may be of
interest. For example, your company likes to gauge sales during a
certain time of year and to keep costs low to a point that the business
is making money. These various statistical measurements are important in
the world of statistics because they help you make general conclusions
about a given population or sample.
To assist in your analysis for Silver’s Gym, answer the following questions about the Body Fat Versus Weight data set:
Click here to download the Body Fat Weight data set.
- In some data sets, the mean is more important than the median.
For example, you want to know your mean overall grade average because
the median grade average would be meaningless. However, you might be
interested in a median salary to see the middle value of where salaries
fall. Explain which measure, the mean or the median, is more applicable
for this data set and this problem.
- What is the importance of finding the range/standard deviation? Why might you find this information useful?
Part II: Hypothesis Testing
Organizations sometimes want to go beyond describing the data and
actually perform some type of inference on the data. Hypothesis testing
is a statistical technique that is used to help make inferences about a
population parameter. Hypothesis testing allows you to test whether a
claim about a parameter is accurate or not.
Your boss makes the claim that the average body fat in men attending
Silver’s Gym is 20%. You believe that the average body fat for men
attending Silver’s Gym is not 20%. For claims such as this, you can set
up a hypothesis test to reach one of two possible conclusions: either a
decision cannot be made to disprove the body fat average of 20%, or
there is enough evidence to say that the body fat average claim is
To assist in your analysis for Silver’s Gym, consider the following
steps based on your boss’s claim that the mean body fat in men attending
Silver’s Gym is 20%:
- First, construct the null and alternative hypothesis test based on the claim by your boss.
an alpha level of 0.05, perform a hypothesis test, and report your
findings. Be sure to discuss which test you will be using and the reason
for selection. Recall you found the body fat mean and standard
deviation in Part I of the task.
- Based on your results, interpret the final decision to report to your boss.