Question

You are doing research on balance and fitness. It is known that the time a person can stay balanced in a certain yoga pose is normally distributed with a mean of µ = 68 seconds and a standard deviation of α = 20 seconds. To complete this project, you will use the attached Excel file for data from a sample of 20 athletes. There are three variables: 1) The time the subject stayed balanced 2) The number of days per week the subject stayed balanced 3) The favorite exercise of the subject Descriptive Statistics You will analyze your data and compute the following statistics for the sample: 1) The Mean and Standard Deviation of the number of seconds the subject stayed balanced 2) The Median number of days per week exercised 3) The Mode of the favorite exercise 4) The percent of the subjects that stayed balanced longer than 75 seconds Probability You will analyze your data and compute the following probabilities: 5) The probability of selecting a subject at random with a favorite exercise of running 6) The probability of selecting a subject at random with a favorite exercise of squats or they exercise more than 5 days per week 7) The probability of selecting a subject at random with a favorite exercise of cardio and they exercise 1 day per week 8) Assume that the probability of an athlete exercising less than 3 days per week is 30%. Use the number of days per week of your first subject as x in the following calculation. Determine the probability of x out of 20 subjects exercised less than 3 days per week. Hypothesis Testing Imagine this is your original research. Write a one-paragraph introduction to your research, discuss how you would select your sample (is it a random sample?) and identify your hypothesis regarding the amount of time your athletes will stay balanced. Present all your raw data and statistics in an organized manner (copy and paste from Excel is acceptable). Write a one-paragraph conclusion about your overall project. You will analyze your data and include the following information: 9) Identify your Null and Alternate Hypotheses using math symbols 10) Identify the α level you chose 11) If you are using a traditional hypothesis test identify the critical z-score 12) Calculate your test statistic 13) If you are using the P-Value Method identify your P-Value 14) Determine your decision based on your critical z-score or your P-Value 15) Write a concluding statement based on your decision Important Instructions: The Excel file will repopulate every time you open it or enter anything in the file. Once you open the file copy and paste the data into a Word document, and save it labeled Project Data. Now you can use the data to complete the Final Project. REFER to the RUBRIC below to ensure you submit all of the required components.

Answer 1

1) The Mean and Standard Deviation of the number of seconds the subject stayed balanced

Mean = µ = 68

Standard Deviation = σ = σ/√n = 20/√20 = 4.47

2) The Median number of days per week exercised

The median number of days = Mean = 68

3) The Mode of the favorite exercise

Mode of the favorite exercise = Mean = 68

In a normal distribution, Mean = Median = Mode

4) The percent of the subjects that stayed balanced longer than 75 seconds

z = (x - µ)/σ/√n = (75 - 68)/20/√20 = 1.57

P (z > 1.57) = 0.0588