You have been asked to design an experiment examining the effect of 4 different diets on weight loss in sedentary volunteers. You will be using a brand new device to measure their body fat mass in the volunteers. The device manufacturer has given you a calibration sample of known fat mass to test the machine.

Write a 1500 word essay to explain how you would use statistical techniques to design and analyse an economical experiment. Justification of methods used is recommended. Part of your answer should outline how you would communicate the results of the study to both lay and scientific audiences.

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The database for the analysis is from a national survey of 1,924 line-level jail staff, which was conducted through a collaborative endeavor between the Center for Innovative Public Policy and the American Jail Association, with funding from the Bureau of Justice Assistance (U.S. Department of Justice). Although not randomly generated, respondents represent 46 states and are generally reflective of what is known about the composition of the national line officer jail workforce in terms of demographics. We are going to use the database of line-level jail employees to assess the impact of both work-related variables and personal characteristics on the intention of employees to resign.

1. The dependent variable is commitment to the current agency (jail). Respondents indicated:  1) They are not committed to working at their current jail; or 2) They are committed to working at their current jail.

2. Choose 3 of these 9 independent variables (with a response of No or Yes) to use in your hypotheses:

1. Being paid what my skills, education and experience are worth

2. Being proud to work here

3. Enjoying a positive work climate on the job

4. Having a say in how things are done here

5. Having input into decisions that affect me

6. Knowing that management listens to my opinions

7. Feeling appreciated by my supervisor

8. Being respected by those above me in the chain of command

9. Having opportunities for promotion

1. The two control variables are gender and education level.  Choose one of the control variables to use in your hypotheses.

2. Develop a hypothesis for each of the three independent variables and the one control variable (i.e., Jail staff who work in a positive work climate are more likely to be committed to their current agency than are those who do not work in a positive work climate, while controlling for gender).

2. A sample of 81 observations is taken from a normal population with a standard deviation of 5. The sample mean is 40. Determine the 95 percent confidence interval for the population mean.

8. Dr. Patton is a profressor of English. Recently she counted the number of misspelled words in a group of student essays. She noted the distribution of misspelled words per essay followed the normal distribution with a population standard deviation of 2.44 words per essay. For her 10a.m. section of 40 students, the mean number of misspelled words was 6.05. Construct a 95 percent confidence interval for the mean number of misspelled words in the population of student essays.

10. Use appendix B.2 to locate the value of t under the following conditions:

a. The sample size is 15 and the level of confidence is 95 percent.

b. The sample size is 24 and the level of confidence is 98 percent.

c. The sample size is 12 and the level of confidence is 90 percent.

*****FYI in order to answer this questions please reference to B.2 student’s t distribution (concluded)found in this link http://www.wiziq.com/tutorial/11174-Tablas-de-Estadisticas*****

12. The U.S. Dairy industry wants to estimate the mean yearly milk consumption. A sample of 16 people reveals the mean yearly consumption to be 60 gallons with standard deviation of 20 gallons.

a.What is the value of the population mean? What is the best estimate of this value?

b.Explain why we need to use the t distribution. What assumption do you need to make?

c. For a 90 percent confidence interval, what is value of t?

d. Develop the 90 percent confidence interval for the population mean.

e. Would it be reasonable to conclude that the population mean is 63 gallons?

16. Ms. Maria Wilson is considering running for mayor of the town of Bear Gluch, Montana. Before completing the petitions, she decides to conduct a survey of voters in Bear Gulch. A sample of 400 voters reveals that 300 would support her in the November election.

a. Estimate the value of the population proportion.

b. Develop a 99 percent confidence interval for the population portion.

c. Interpret your findings.

20. We want to estimate the population mean within 5, with a 99 percent level of confidence. The population standard deviation is estimated to be 15. How large a sample is required?

22. The estimate of the population proportion is to be within plus of minus .10, with a 99 percent level of confidence. The best estimate of the population proportion is .45. How large a sample is required?