Sungho YoonPublic Health 391BNov. 9 2015Assignment 4Instructions: The following questions test your understanding of thelecture material on Foundations for Inference. You must show yourwork, meaning you must report your calculations and not just theanswers. You will NOT receive full credit if you do not show yourcalculations where appropriate. Additionally, I do not expect this to bewritten in a paper format. In other words, your document should havethe questions written first, then the answers following. You will NOTreceive full credit if you do not list the questions and the answers. Aftercompleting the assignment, upload your answers as a docx or PDF file(e.g. Zhang_hw4.docx or Zhang_hw4.pdf). The final date to submit thisassignment and receive full credit is by 9am on Nov 9th , 2015. The finalday to submit the assignment for partial credit (-20%) is by 9am, Nov 13th,2015. Hypothetical Scenario: Recent evidence suggests that resistance training(RT) may reduce metabolic and cardiovascular disease risk, even amongoverweight individuals.To test this hypothesis, researchers investigated whether overweightindividuals with high strength fitness exhibit cardiovascular/metabolicphenotypes similar to normal-weight individuals with high strength fitness.In a random sample of 150 overweight individuals with high strengthfitness, mean pulse wave velocity (PWV), a measure of arterial stiffness,was 800 cm/s with a standard deviation of 230 cm/s. Previous research hasindicated that for normal weight individuals with high strength fitness,mean PWV is 820 cm/s.1. State the null, one-sided, and two-sided hypotheses in the context of the problem. (3 points)- Null – H(0): u = 820- One-sided – H(0): u = 820 - H(A): u > 820 P = 0.1434- Two-sided – H(0): u = 820 - H(A): u does not equal to 820 P = 0.1434 * 2 = 0.28682. Based on the data what is the point estimate of the mean pulse wave velocity? (2 point) - 800 that overweight individuals with high strength fitness 3. State the assumptions and conditions for calculating a 95% confidence interval and calculate the lower and upper limits of the 95% confidence interval. (6 points) - H(0): MAS of overweight individuals = MAS of normal weight individuals = 820 - H(A): MAS of overweight individuals does not equal to MAS of normal weight individuals = does not equal to 820 - SE = 230/ root (150) = 18.78- CI = 800 + 1.96 * 18.79 = 836.8, 800 – 1.96 * 18.78 =763.24. Based on the 95% confidence interval, do you have sufficient evidence to reject the null hypothesis? Briefly explain (in 1-2 sentences) why or why not. (3 points)- 820 is within the range of the 95 % CI for the random sample of 150 overweight individuals with high strength fitness. Thus it is plausible that overweight fitness have average pulse wave velocity, a measure of arterial stiffness equal to 820. So, we fail to reject the null that average overweightindividuals with high strength fitness equal to the average of normal weight individuals with high strength fitness.5. Calculate the p-value using the α=0.05 level of significance for a two-sided hypothesis.Explain in 1 - 2 sentences whether you have sufficient evidence to reject the null hypothesis. (6 points)- Two-sided – H(0): u = 820 - H(A): u does not equal to 820 P = 0.1434 * 2 = 0.28682-sided p-value = 0.2868. If the overweight individuals with high strength fitness are 820, there is less than 28.68% chance of observing a random sample of 150 overweight individuals with a measure of arterial stiffness of 800. Since 0.2868 > 0.05 it does not provides enough sufficient evidence to reject H(0) in favor of