Statistics Assignment

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?