General Instruction: Answer the problems given below. Show your complete solution and illustrations (if there is). 1. Suppose the following data are selected randomly from a population of normally distributed values with unknown variance. 40 39 45 45 49 41 47 44 56 53 39 42 44 38 57 58 a. Compute the mean and standard deviation. b. Construct a 90% confidence interval to estimate the population mean u. c. Find the lower and upper confidence limits. d. Interpret the interval. 2. Independent random samples were selected from two populations with unknown and unequal variances. Population 1 Population 2 1 = 18 n- = 12 X = 8.15 T = 6.15 s, 2 = 4.2 $ 2 = 2.4 Construct a 90% confidence interval to estimate the difference in the population means #1 - Hz. 3. A study is conducted to compare the performance of students with more than one personal electronic gadget and those with only one. A number of them were taken as subjects for the study. The mean grades of these students and these standard deviations are shown below. Students Mean Standard deviation Sample size With one gadget X1 = 83 $ = 12 n, =7 With more than one gadget *, = 79 $2 = 13 n, = 5 Is it possible to conclude that there is no significant difference in the mean grades of the two types of students at a 95% confidence level