Using the data set provided, follow the following directions and reply to each question below.

Please make sure to always use proper statistical notation in your answers.

1.Define your population of interest:

(what does the data represent)

2.Why is it important for you to have a random sample from the population of interest?

3.Using StatKey (or Excel) find the original random sample's mean(use proper notation)

4.Using StatKey (or Excel) find the original and representative sample's standard deviation (use proper notation)

5. attached below.

6.Now, still using StateKey make a Bootstrap Sampling distribution of at least 3003 samples

Take a picture of your distribution and paste it

7.Picture attached below.

8.What does each dot in the Bootstrap Sampling Distribution represent?

9.What is the 90% Confidence Interval given this Bootstrap Sampling Distribution?

(Please paste the image of the 90% Confidence Interval here)

10.What is the 95% Confidence Interval given this Bootstrap Sampling Distribution?

(Please paste the image of the 95% Confidence Interval here)

11.Interpret the 95% Confidence Interval - what does it represent in context?

Please explain with a full sentence what the 95% C.I. represents concretely.

12.If you wanted to use a Theoretical Statistical Distribution (instead of a Bootstrap Sampling Distribution) to identify the 95% Confidence Interval, what assumptions would you need to check to be able to do so?

State these assumptions then show if they are met in your case.

13.Using the Theoretical Statistical Distribution, find the 95 % Confidence Interval following these steps:

a)Identify the Test Statistic you would use in this case and explain why:

b)Find the Standard Error: (show the formula you used and indicate your final answer using proper notation)

c)Find the Margin of Error for your 95% Confidence Interval (show the formula you used and indicate your final answer using proper notation- do not use the rule of thumb)

d)Find the 95% Confidence interval: (show the formula you used and indicate your final answer using proper notation)

14.Assuming that the true Population mean is equal to approximately 4200, with a standard deviation of about 1980 does your Confidence Intervals provide a realistic estimate for the true population mean in both the Bootstrapping and Theoretical approaches or not? Explain

Let's assume that you wanted the margin of error associated with your 95% confidence Interval to be no more than 250, how large would your sample size need to be in this case?

(show the formula you used and indicate your final answer using proper notation. Show all your work)

\f\f7. Describe this Bootstrap Sampling Distribution Shape, center, and variability given to you by W Use proper notation. Symbol (if Measure applicable) Shape of the m distribution: Center of the Distribution Variability 5. Using this representative w you have selected use mm create three Bootstrap samples and find for each Bootstrap sample the mean. Then read the standard error associated with the corresponding Bootstrap Sampling Distribution created by three Bootstrap Samples. Record your data for the first three Bootstrap samples you select, in the table below Bootstrap Bootstrap Bootstrap Bootstrap Bootstrap sample sample Sample Sample Sampling size statistic measure Distribution of measure of variability variability Number 1 Number 2 Number 3