Question

2. For the following data: 2 3 4 5 6 12 10 9 8 5 13 a. Calculate the sample mean and sample variance b. Calculate the probability that the population mean is between 9 and 10 if the population standard deviation is known to be 3. c. What is the 90% confidence interval for the population mean if the population standard deviation is known to be 3? d. Calculate the 90% confidence interval using the sample standard deviation.

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Abdul-Rahim Taysir

Answer 1

Data 1 2. 3 5 6 12 10 a 8 5 13 a) Sample ole Mean ał = 1 Exe (12 400 +9+8+5 +13) 6 12 Sample ole variance S² = L E Cx - 7² [ (12-105) * - _ (13-4a53a] † (25 + os * 0.5² tras? 4405² +352) : 8.3 =) S = 2.88. b) Prob. of pop. mean interval 2-2 % confidence of the interval an (9, 10 ZX ă+Zx 5 here, x = 9.5 0-3 nas 2x 5 = 6.5 = 2x3 = 0,5 => 2 -0.37 asing 2-score, P(-2<xcz ) PC-037 CX 20237) = 0 .288

x = = 0.5 = 2x3 = 0.5 -> Z-0.37 1.645 va using z-seone P(-2LXL2) - P(-0.37 EXC0237) = 0 .288 c) 90% confol- interwal using pop. variance 2-score for 90% [ 3-25, 2+28 [ 9.5-10646 *, 9,5+164573 [763, 1667) d] 90% interval using sample (t-disth" as dof: n-1=4 in-1= 4, &- (1 -0.9 2-61-0.9=0,05 t-table for dof= 4, x=0.05 t = 2.132. [e-text] • [9.5 -2.1324872, 9.5 +2.3zXV6-3 [6.753 12.246), mean using -