Question

please do not use software or excel to solve this

An experimenter wanted to check the variability of measurements ob- tained by using equipment designed to measure the volume of an audio source. Three independent measurements recorded by this equipment for the same sound were 4.1, 5.2, and 10.2. Estimate the confidence interval for o2 at confidence level 1 - a=0.9.

Answer 1

let x.. Measurments 16.81 5.2 10.2 27.04 104.04 Mean = 5€ = 3x - 19.5 = 6.5 Sample variance (s')(I x?-nă) => (147.89 - (3)(6-5)-) s² = 10.57 90% onfidence interval for r² is as follows: (n-1)s? << (n-ns? x 212 x 1-2/2 T²2 (3-1) (10.57) (3-1) (10.57) xos xo.gr kr < 2 * 10.57 16156 S.9915 (2) (10.57) 0.1096 16156 3.5283 <r < 192.8832 2 Confidence interval for 3 (3.5283, 192.8832 ) using Excel (Hint: Yeos = 5.9915 = 0.1096 using Excel = CHIINV (O.os,2) = CHIINV (0.gs.2) ] žogs