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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. Notice you are to calculate the mean, median, range, and standard deviation for the body fat and for the weight.
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 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 inaccurate.
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.
- 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. 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.