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Assume that :7: and 3 remain the same as in the problem 1 in the homework. But the sample size (n) changed to 15. Construct a 95% confidence interval for the population mean p. O (3.13, 6.87) O (2.52, 7.57) O (3.74, 6.26) O (2.81, 7.19) 04 Problem 4 1 Point Consider the same setting as in the problem 2 of the homework assignment. Construct the 95% condence interval for the population mean. 0 (2.11, 7.11) O (1.55, 7.67) O (2.56, 6.96) O (2.33 6.89) Homework 3 1. The following random sample was selected from a normal distribution: 4,6,3,5,9,3. a. Construct a 90% confidence interval for the population mean u. x+tim x= ExI n t= tn-18/2 CI= x + ta/2 4 + 6 + 3 ... + 3 = 30 - 5 x = 5 6 degrees of freedom : S = VL, E ( x, - x ) def = n-1 6 -1=5 = = [(4- 5)2 + 16+ 5 )?.. + ( 3-5)2 ] The critical value at 0. 10 level for 5 degrees of = = [Itl+ 4 .... + 4 freedom is 2.015 5.2 CI = x + tap ( fx) S = 2. 28 = S+ 2.015 /2.28 6.88 = 5+ 2. 015 ( 0. 931 ) or 0% confidence interval is 3. 124 6. 876 = (3. 124, 6. 876 ) b. Construct a 95% confidence interval for the population mean M. 2 = 1 - 697,00) = 0. 05 +12 : 0.05 = 0.025 xz t + = tn-1 8/ 2 = 6 5, 0.025 = 2. 57 05 5+ 2. 570 5 ( 2 . 28 5 + 2. 39 = 7.39 ( T - table ) 5 - 2. 39 = 2.61 95% confidence interval is ( 2 . 6 7. 39