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Project - Silver Gym Part 1-4 Analysis

Question # 00010487
Subject: Statistics
Due on: 03/19/2014
Posted On: 03/18/2014 09:07 PM

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Actual calculations for figuring these numbers in this example you provided for part 1 and to of Silvers GYM? with graphs depicting where needed example;

PART 1

    • 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 2
    • 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.

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:

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.

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, yourxversusyvariables. 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? Discuss the strength of the correlation coefficient calculated, and if the correlation is positive or negative.

  • 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 is zero. 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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Project - Silver Gym Part 1-4 Analysis

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Tutorial Preview …one xxxxx simply xxxxxxx the weight xx an individual, xxx then xxx xxx equation xxxx the linear xxxxxxxxxx to make x prediction xxxxx xxxx fat xxxxx Excel, construct x scatter plot xx your xxxx xxx accompanying xxxxx file Using xxx graph and xxxxxxxxxx determine xxxxxxx xxxxx is x positive correlation, x negative correlation, xx no xxxxxxxxxxx xxx did xxx come to xxxx conclusion? The xxxx points xx xxx graph xxxxxx to tend xx move upward xx the xxxxx xx the xxxxxx increases This xxxxxxxxx a positive xxxxxxxxxxx between xxxxxx xxx body xxx percentage Calculate xxx correlation coefficient, xx and xxxxxx xxxx conclusion xxxx your scatter xxxx What does xxx correlation xxxxxxxxxxx xxxxxxxxxx The xxxxxxxxxxx of the xxxxxxxxxxx coefficient is xxxxx in xxx xxxxxxxxxxxx Excel xxxx The result xx r = x 6132 xxx xxxxxxxx sign xx the result xxxxxxxx that the xxxxxxxxxxxx is xxxxxxxx xxx value xx 0 6132 xxxxxxxxx that the xxxxxxxxxxxx is xxxxxxxxxx xxxxxx Add x regression line xx your scatter xxxxx and xxxxxx xxx regression xxxxxxxx See the xxxxx in the xxxxxxxxxxxx Excel xxxx xxxx the xxxx appear to xx a good xxx for xxx xxxxx Why xx why not? xxx line is x moderately xxxx xxx for xxx data in xxxx it follows xxx trend xxxxxxxx xxxxx are xxxx points which xxxxxxx significantly from xxx trend xxxxx xxx a xxx points that xxxxx be considered xx be xxxxxxx xxxxxx or xxxxxxxx Regression equations xxxx you make xxxxxxxxxxx Using xxxx xxxxxxxxxx equation, xxxxxxx what the xxxxx means, and xxxxxxxxx the xxxxxxxxx xxxxx of xxxx fat (y) xxxx weight (x) xxxxxx 0 xxxxxxxxx xxx meaning xx this equation xxx regression equation xxxx the xxxxx xx y x 0 1617x x 9 9952 xxx slope xx xxx regression xxxx is 0 xxxxx indicating that xxx each xxxxxxxxxx xxxxx of xxxxxxx the body xxx percentage increases xx…
Attachments
SilversGym_-_Part_I-IV_Analysis.docx (130.84 KB)
Preview: extreme xxxxxx to xx discarded The xxxxxxxx deviation value xx also xxxx xx calculating xxx test statistic xxxxx in hypothesis xxxxxxx Part xxx xxxxxxxxxx TestingThe xxxxxx Gym manager xxxxx the claim xxxx the xxxxxxx xxxx fat xx men attending xxxxxxxxxx Gym is xxx You xxxxxxx xxxx the xxxxxxx body fat xxx men attending xxxxxxxxxx Gym xx xxx 20% xxx claims such xx this, you xxx set xx x hypothesis xxxx to reach xxx of two xxxxxxxx conclusions: xxxxxx x decision xxxxxx be made xx disprove the xxxx fat xxxxxxx xx 20%, xx there is xxxxxx evidence to xxx that xxx xxxx fat xxxxxxx claim is xxxxxxxxxx To assist xx your xxxxxxxx xxx Silver’s xxxx answer the xxxxxxxxx questions based xx your xxxxxxxx xxxxx that xxx mean body xxx in men xxxxxxxxx Silver’s xxx xx 20%:First, xxxxxxxxx the null xxx alternative hypothesis xxxx based xx xxx claim xx your boss xxxxx an alpha xxxxx of x xxx perform x hypothesis test, xxx report your xxxxxxxx Be xxxx xx discuss xxxxx test you xxxx be using xxx the xxxxxx xxx selection xxxxx on your xxxxxxxx interpret the xxxxx decision xx xxxxxx to xxxx boss Hypothesis xxxxxxxx null and xxxxxxxxxxx hypotheses xxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx hypothesis:Critical xxxxxxxxxxxx on the xxxxxxxxxx shown above, xxx test xx x two-tailed xxxx The z-statistic xxx be used xxxxxxx the xxxxxx xxxx is xxxxxxx than 30 xxx critical values xxx a xxxxxxxxxx xxxxxxx with x = 0 xxx are -1 xx and x xx This xxxx will reject xxx null hypothesis xx the xxxx xxxxx is xxxx than -1 xxx orgreater than x 96Test xxxxxxxxx xxxx value xx calculated as:The xxxxxxx for this xxxx statistic xx x 0297 xxxxxxxxxxxx test value xx less than xxx negative xxxxxxxx xxxxxx -1 xxx so the xxxxxxxx is to xxxxxx the xxxx xxxxxxxxxx Using xxx.....
SilversGym_-PartI_WOrksheet.xls (86 KB)
SilversGym_-_Part_III_IV_Worksheet.xlsx (40.59 KB)
Preview: and x mean xxxx fat percentage xx 18 94% xxx standard xxxxxxxxx xxx body xxxxxx was 29 xx pounds, while xxx standard xxxxxxxxx xxx body xxx percentage was x 75% The xxxxx for xxxx xxxxxx was xxx 65 pounds xxx the range xxx body xxx xxxxxxxxxx was xx percent The xxxxxx values for xxxxxx and xxxx xxxx respectively, xxxx 176 5 xxxxxx and 19 x percent x xxxxxxxxxx test xxx performed to xxxxxxxxx if the xxxx supported x xxxxx that xxx mean body xxx percentage was xxx The xxxxxx xx that xxxx was that xxxxx was not xxxxxxxxxx evidence xx xxxxxxx that xxxxx at the x 05 level xx significance x xxxxxxxxxx analysis xxx also performed, xxx resulted in xxx following xxxxxxxx xxxxxxxx body xxx to weight:The xxxxxxxxxxx coefficient was xxxxx to xx x 6132, xxxxx indicated a xxxxxxxxxx strong positive xxxxxxxxxxxx between xxxxxx xxx body xxx percentage BODYFAT xxxxxxxxx (y)Because it xx much.....
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