Problem 1 Part 1 In a clinical study. 1000 subjects were vaccinated with a vaccine manufactured with a new ingredient. Over a period of roughly 23 weeks. 6 of these subjects developed the u. a] Find the point estimate of the population proportion that were vaccinated but still developed the u. Specify its value and statistical notation for this estimate. b] Show set up {formula with numbers plugged in] and verify that the standard error of this estimate is 0.0024. Briey explain what this number means. c] What is the value of z-multiplier 2m"? for a 98% condence interval? Find the margin of error for a 98% confidence interval. Round your margin of error to the nearest four decimal places. Problem 1 Part 2 d] Use your answers from Problem 1 Part 1 and construct a 98% conlidence interval. Interpret. e] Based on your conlidence interval. is it plausible that less than 1% of all people vaccinated with the vaccine will develop the flu? Explain. Problem 2 Refer to the Problem 1. Does the information provided in Problem 1 satisfy conditions [assumptions] of the large number condence interval for 3.)? State two assumptions and determine whether each is met or not. (Hint: See lecture notes on page 108. There are two assumptions.) Problem 3 An election is expected to be close. Pollsters planning an exit poll want their estimates to be to within :l:.l'l2 with 90% condence. How large should be the sample size if they have no prior information? Problem 4 Part 1 The 2012 General Social Survey asked, "What do you think is the ideal number of children for a family to have?". The 590 females who gave a numeric response from 0 to 6 had a median of 2, a mean of 2.56, and a standard deviation of 0.84. a) What is the point estimate of the population mean? Specify its value and statistical notation for this estimate. b) Find the standard error of this estimate. Round your answer to the nearest four decimal places. Explain what this number means. c) What is the value of t-multiplier /2n- for a 99% confidence interval? Find the margin of error for a 99% confidence interval. Round your margin of error to the nearest two decimal places. Problem 4 Part 2 d) 99% confidence interval is (2.47, 2.65). Interpret the interval in context. e) Is it plausible that the population mean of females' ideal number of children is greater than 2? Problem 5 Refer to Problem 4. State assumptions of the confidence interval for the population mean. Determine whether each assumption is met based on Problem 4 description. Explain. Problem 6: Multiple Choice Question The following interprets the 99% confidence interval for population mean of females' ideal number of children from Problem 4 part d) (2.47, 2.65). Which of the following is correct? (A) In the entire population, 99% of females' ideal number of children fall within 2.47 and 2.65. (B) We are 99% confident the sample mean of females' ideal number of children falls between 2.47 and 2.65. (C) If we repeatedly sample 590 females randomly and construct 99% confidence intervals, then in the long run, 99% of those intervals contain the population mean of females' ideal number of children. (D) There is 99% probability population mean is between 2.47 and 2.65