Question

Subject	Balance Time (sec)	Number of Days Exercise	Favorite Workout
1	21	2	Cardio
2	50	6	Running
3	40	1	Running
4	123	1	Running
5	71	3	Squats
6	115	2	Cardio
7	29	6	Weights
8	77	5	Squats
9	95	2	Cardio
10	90	7	Squats
11	11	1	Cardio
12	47	6	Running
13	51	5	Running
14	87	5	Squats
15	66	2	Squats
16	42	3	Weights
17	29	1	Cardio
18	80	2	Cardio
19	62	4	Cardio
20	11	7	Squats

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

Answer 1

According to Chegg answering guidelines giving answer to first 4 questions.

Thank you.