Question

13-14. A 99% confidence interval (in inches) for the mean height of a population is 65.7<<67.3. This result is based on a sample of size 144. Construct the 95% confidence interval.

Please show work step by step. and round answers to 4 decimal places. thank you!

Answer 1

65.75 Ansurer: 99.4. Of. Confidence interval for Menn height is given as: uf <67-3 X-tx.df [ standard Error x + to, O (standard Eror ) . 67-3 65.7 TA lie, В Sample Size n 144 144-1-1143 Degree of freedom - Doan-i where, 2.611 from T- Critical valze Calculcitor Toto of to,n-1; +0.005, 143 So, level of Significance K - I- 99.). 1-C1 x 1- 99 100 1- 0.99 0.01 X 0.01 2 0.005 2 Add: from ② 8 B => 27 - 65.7+ 65.7+ 67.3 =) 25 133 = --> Х 133 2 => 66.5

Substract [4 Ô from © [X + ty, n-1 (standard Eror)] - [ 8-tgi n-(stenokard Error) 67.3 - 65.7 1.6 standard error => 2x Х tą, n-1 standard Error 1.6 2x to n-1 1.6 1.6 0.3063 2X2.611 5.222 standard Error ul Similarlly, 95% Confidence interval for is given as Calculate : (x+ to De * Standard Error) So, level of Significance - 1-C.I xa la 95% 1- 95 100 x = -0.95 x 0.05 Ź - 0.05 = = 0.025 2 DE => Degree of freedom n-1 144-1 Do 143;

from T-Critical value Calculator T- to.025, 143 1.976 ( I - Value) 95.1 of CI * Ito Of * Standard Error where i 66.5 tx, Dp @ 95').C.ID 1.976 standard Error 0.3063 So, 66:5 + 1.976 * 0.3063 66-5 + 0.6052488 lower Boundary limit 66.5 0.6052488 65.8947 Upper Boundary linnit 665 + 0.6052488 67.1052 ; 21 [ 95.. OF CI (65-8947; 67.1052] [ 65 65-9; 67.1] Please rate my werk, if the response is helpful Kindly Support Subject foperts with your Valable feedback.... Stay safe. keep henthy Thank you ;