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. •Calculate the mean, median, range,
and standard deviation for the Body Fat Versus Weight data set.
Report your findings, and interpret the meanings of each
measurement. •The measures of central tendency are important in
real-world situations. ◦What is the importance of finding the
mean/median? Why might you find this information useful? •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. •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 inaccurate. To
assist in your analysis for Silver’s Gym, answer the following
questions 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. •Using
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. •Based on your results, interpret the final
decision to report to your boss.
Part III: Regression and Correlation
Based on what you have learned from your research on
regression analysis and correlation, answer the following questions
about the Body Fat Versus Weight data set:
When performing a regression analysis, it is important to
first identify your independent/predictor variable versus your
dependent/response variable, or simply put, your x versus y
variables. How do you decide which variable is your predictor
variable and which is your response variable?
Based on the Body Fat Versus Weight data set, which variable
is the predictor variable? Which variable is the response variable?
Explain.
Using Excel, construct a scatter plot of your data.
Using the graph and intuition, determine whether there is a
positive correlation, a negative correlation, or no correlation.
How did you come to this conclusion?
Calculate the correlation coefficient, r, and verify your
conclusion with your scatter plot. What does the correlation
coefficient determine?
Add a regression line to your scatter plot, and obtain the
regression equation.
Does the line appear to be a good fit for the data? Why or
why not?
Regression equations help you make predictions. Using your
regression equation, discuss what the slope means, and determine
the predicted value of weight when body fat equals 0. Interpret the
meaning of this result
Part IV: Putting it Together
Your analysis is now complete, and you are ready to report
your findings to your boss. In one paragraph, summarize your
results by explaining your findings from the statistical measures,
hypothesis test, and regression analysis of body fat and weight for
the 252 men attending Silver’s Gym.
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