Question

Find a confidence interval for μ assuming that each sample is from a normal population. (Round the value of t to 3 decimal places and your final answers to 2 decimal places.) (a) x⎯⎯ x ¯ = 25, s = 5, n = 7, 90 percent confidence. The 90% confidence interval is to (b) x⎯⎯ x ¯ = 50, s = 4, n = 19, 99 percent confidence. The 99% confidence interval is to (c) x⎯⎯ x ¯ = 121, s = 14, n = 29, 95 percent confidence. The 95% confidence interval is to

Answer 1

We know that, the confidence interval for population mean when is unknown given by, х + s tn-1,0% = 25, S = 5, n=7, 1-9 = 0.90 *= 0.10 . The go% C.I is, ( 25 25 7 5 / 5 x 1.943 Here, tn-luth tat, Out = to,o.os = - T.INV (0.05,6) 1.943 - {Using MS-Excel ( 25 + . The go % } C.I. is , 3.67 =(21033, 28167) ] 6 x = 50, 5=4, n= 19, |-* = 0.99 = K = 0.01 . The 99 % C. I. is, 50 + X 2.878 Here, tn.1,& Jig tig, oool 2 t 18,0.005 = - T. INV (0.005,18) 2.878 { Using MS-Excel ... The go % GI. is, (50 7 2.64) こ = (47.36, 52.64

© x=121, 5=14, n=29, 1-x=0.95 2x=0.05 .: The 95% C.I is, $ 121 14 x 2.048 129 Here, to-1,*/ t 2gt, ovos t28, 2 28, 0.025 = - T. INV (0.025,28) = 2.048 –{using Ms-Excel} .. The gs % C.I is . (121 7 ={( 115.68, 126.32) 5.32)