Question

Consider a normal population with an unknown population standard deviation. A random sample results in x = 42.55 and 52 = 28.09. [You may find it useful to reference the t table.] a. Compute the 99% confidence interval for u if x and s2 were obtained from a sample of 24 observations. (Round intermediate calculations to at least 4 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.) Confidence interval b. Compute the 99% confidence interval for p if x and s2 were obtained from a sample of 26 observations. (Round intermediate calculations to at least 4 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.) Confidence interval c. Use your answers to discuss the impact of the sample size on the width of the interval. The bigger sample size will lead to a larger interval width and therefore a more precise interval. The bigger sample size will lead to a smaller interval width and therefore a more precise interval.

Answer 1

Page No Date. Solution!. Given that, Š? = 128.09 = 5.3 x=42.55 s = 5.3 n = 24 df = n-1 = 24-1 =23 a) At aq % confidence level the tis x=1- 99 % x=1-0.99 = 0.01 Q = 0.24 -0.005 tai df=t0005; 23 = 2.807 At aq % confidence interval for ais At aa olo con tap 2: df te Vn V24 42.55 + 2.807 x 5.3 42.55 € 3.04 (39.51, 45.59) The aq olo confidence interval for ais ([ 39.51 ] to ( 45. 597)

PER Page No: Date. اط n = 26 df = noi = 26-1=25 At 99 % confidence Level the t is x=1- qq to x=1-0.99 = 0.0L a = 0.0l = 0.005 tarz; df = to.oos; 25 = 2: 787 At 99% confidence interval for eis x t ta, zi dF XS 42.55 = 2.787 x 5.3 V26 42.55 I 2.90 (39.65, 45.45) The 99 % confidence interval for un u IS ( 39.65] to ( 45.451) c) The bigger sample size will lead to a lager interval width and therefore a more precise interval is. Answer-part (A2