Question 4 (6 points) Assume you have a random sample of 350 people and constructed a 90% confidence interval. a. (3 pt) If the sample size was increased to 500, keeping all other values the same, what would happen to the center and width of the interval? Would they stay the same, get smaller, or larger? Explain. b. (3 pt) If you increase the confidence level to 95%, keeping all other values the sam, what would happen to the center and width of the interval? Would they stay the same, get smaller, or larger? Explain Paragraph V BIUA EVEV + .. . 11:55 AM 99 + O 5/12/2022 DELLQuestion 5 (8 points) Sally is confused. She has constructed a 99% confidence interval for the average age of students at her school and the 99% confidence interval she constructed is (18.4, 25.6). However, she was checking her work, and when she looked at her data, only 37% of the people in her survey have ages between 18.4 and 25.6. a. (2 pt) What is the correct symbol for the mean in Megan's survey? b. (2 pt) What is the sample mean (midpoint)? c. (2 pt) What is the margin of error (half-width)? e. (2 pt) Did Megan make a mistake? In other words, should the proportion of ages contained between 18.4 and 25.6 be 90% or is this a misunderstanding on Megan's part? Explain. BIUA ! . . . Paragraph V + v 99+ 11:56 AM O 5/12/2022 17 DELLQuestion 6 (3 points) The authors collected 1000 pennies of various ages, with an average age of 12.26 yrs. For each of the following descriptions of a sampling distribution, give the letter of the diagram that is most likely to be the correct simulation results of sampling with that sample size and plotting the averages for the samples. In other words, match a graph with a sample size (i.e. Sample size = 1 corresponds to Graph ?)- Sample size = 1 Sample size = 35 Sample size = 200 A. B. Mean=12.215 Mean=11.029 SD =0 832 SO =0.819 Num samples=300 Num samples=300 99+ 11:57 AM O 5/12/2022 17 DELLA. B. Mean=12.215 Mean 11.029 SD =0.032 SD =0.019 Num samples=300 Num samples=300 40 Count Count 20 20 9 10 11 12 13 10 11 12 13 14 15 Sample means Sample means C. D. 11:57 AM 5/12/2022 17 DELLC. D. Mean=12 280 8 Mean-12.150 SD -1.612 SD =10.107 Num samples= 300 Num sales=300 40 Count Count 20 9 12 15 18 0 20 40 80 Sample means Sample means 11:57 AM 5/12/2022 17 DELL