8. 5.6 One in five 18-year-old Americans has not graduated from high school (The Wall Street Journal, April 19, 2007). A mayor of a northeastern city comments that its residents do not have the same graduation rate as the rest of the country. An analyst from the Department of Education decides to test the mayor's claim. In particular, she draws a random sample of 80 18-year-olds in the city and finds that 20 of them have not graduated from high school. Use Table 1. a. Compute the point estimate for the proportion of 18-year-olds who have not graduated from high school in this city. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) Point estimate _________ b. Use this point estimate to derive the 95% confidence interval for the population proportion. (Round intermediate calculations to 4 decimal places. Round "z-value" to 2 decimal places and final answers to 3 decimal places.) Confidence interval ______to______ c. Can the mayor's comment be justified at 95% confidence? Pick the best choice from the following: Yes, since the confidence interval contains the value 1/5 = 0.20. Yes, since the confidence interval does not contain the value 1/5 = 0.20. No, since the confidence interval contains the value 1/5 = 0.20. No, since the confidence interval does not contain the value 1/5 = 0.20. We use the t distribution to construct a confidence interval for the population mean when the underlying population standard deviation is not known. Under the assumption that the population is normally distributed, find t/2,df for the following scenarios. Use Table 2. (Round your answers to 3 decimal places.) a. A 90% confidence level and a sample of 28 observations. b. A 95% confidence level and a sample of 28 observations. c. A 90% confidence level and a sample of 15 observations. d. A 95% confidence level and a sample of 15 observations. t/2,df _______ _______ ________ _________