Body Fat Statistical Analyst

Part I: Statistical Measures

 

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.

Body Fat:

Mean: 18.9385

 

Median: 19.0

 

Range: 45.10

 

Standard Deviation: 7.7509

Weight:

Mean: (NNN) NNN-NNNN/strong>

 

Median: 176.5

 

Range: 244.65

 

Standard Deviation: 29.3892

 

 

 

The interpretations of these values are:

 

 

 

The mean body fat value of 18.9385 percent means that the average

 

measured body fat percentage in this sample is 18.9385 percent. The mean

 

weight of(NNN) NNN-NNNNpounds means that the average measured weight in

 

this sample is(NNN) NNN-NNNNpounds.

 

 

 

 

 

The median body fat value of 19.0 means that half of the participants in the survey had a body fat percentage greater than 19%, and half of the

 

participants had a measured body fat percentage that is less than 19%.

 

Similarly, the median weight of 176.5 means that half of the survey

 

participants had a weight that was greater then 176.5 pounds, and half of

 

the survey participants had a weight that was less than 176.5 pounds.

 

 

 

The range of 45.10 for the body fat percentages means that the difference between the largest and smallest body fat values in the survey is 45.10. The range of 244.65 for the weights indicates that the difference between

 

the highest and lowest weight measured was 244.65 pounds.

 

 

 

The standard deviation values give an idea of the dispersion of the data in each set. They indicate how close the values in the data set are to the mean

 

of the data set.

 

 

 

 

 

What is the importance of finding the mean/median? Why might you find this information useful? Explain which measure, the mean or the median, is more applicable for this data set.

 

 

 

The mean and median both give an indication of the central tendency of the values in the data set. The mean is computed as the arithmetic average of the values. The mean is useful because it can then be used in hypothesis testing to make statistically significant conclusions about the population represented by the data sample.

 

 

 

The median separates the data set into two equal groups, one consisting of values which are greater than the median, and one consisting of values which are less than the median. The median gives a different view of the central tendency of the data set.

 

 

 

In this particular problem, the values of the mean and the median are approximately equal. Either measure could be use to represent the central tendency of the data set. However, since the mean can be use in hypothesis testing, the mean is more useful.

 

 

 

What is the importance of finding the range/standard deviation? Why might you find this information useful?

 

 

 

The range and standard deviation both give an indication of the spread of the data. These values can be used to determine if any values in the data set are extreme enough to be discarded. The standard deviation value is also used in calculating the test statistic value in hypothesis testing.

 

 

 

Part II: Hypothesis Testing

 

The Silver Gym manager makes the claim which averages the body fat in men attending the 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.

 

 

Hypothesis Test:

 

 

 

The null and alternative hypotheses are:

 

 

 

Null hypothesis: (Claim)

 

 

 

Alternative hypothesis:

 

 

 

 

 

Critical values:

 

 

 

Based on the hypotheses shown above, the test is a two-tailed test.

 

 

 

The z-statistic can be used because the sample size is greater than 30.

 

 

 

The critical values for a two-tailed z-test, with  = 0.05, are -1.96 and 1.96.

 

 

 

This test will reject the null hypothesis if the test value is less than -1.96, or

 

greater than 1.96

 

 

 

Test value:

 

 

 

The test value is calculated as:

The p-value for this test statistic is 0.0297

Decision:

The test value is less than the negative critical value, -1.96, so the decision is to reject the null hypothesis.

Using the p-value method, the null hypothesis is rejected since the p-value of the test statistic, 0.0287, is less than the level of significance, 0.05.

Summary:

The hypothesis test indicates that there is sufficient evidence at the 0.05 level of significance to reject the boss’s claim that the average body fat is equal to 20%.

What I need is this part below:

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?

 

• • • • Regression equations help you make predictions. Using your regression equation, discuss what the slope means, and determine the predicted value of body fat (y) when weight (x) equals 0. Interpret the meaning of this equation.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?

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.