Question

#4. A 95% confidence interval for the lives in minutes) of Kodak AA batteries is 4304 <470. Assume that the result is based on a sample of size 100. a) What is the value of sample mean? b) What is the population standard deviation o? c) Construct the 99%confidence interval: d) If the confidence interval 432 < u < 468 is obtained from the same sample data, what is the level of confidence?

Answer 1

Giveno 95% confidence interval XE = 430 XtE = 470 n=100 using coI a calculate X X sample mean ) - E = 430 + E = 470 X = 900 -1 450 2 4 = 900 - Ans b) calculate » Y - X t standard deviation Co E = 430 = 470 E 40 = 20 ZE = 40 s critical z value y for 95% is 1.96 = 20 = 1.96* Too » 20*110o = 1.96*6 200 = 1.96Ao » o=200/1.96 »o=102004 v Ans.

I 1 Constouct go% CI Formula - X-E < M L X TE where, E = Tc * Critical z value for ggf. is 2.58 2,58 * 102.04 plug formula the value of X & E in the given XE < ll LX te 450-26.33 2 4 2 450 + 26.33 7 423.67 <u< (476.33) Ans. @ Gixené X- E = 432 E = 268 X o=100 x-E=432 X TE=468 t = 465 E = 18 18 E- 2 E = 36 ..75 * 102.04 78 € ZA 102.04 Voo Cutical z value for 92 % confidence level is 1.75 Hence, we get ZC=lns 20% level of confidence/

③ Giveno Lower : Upper : 7- X T E = 48 E = 52 I step. I calculate X & E X - F= 48 XtE =52 XE =48 X + E = 52 2x = 100 x= 100/2 = 50 where o E = 2c * v E ZE=4 = 412 = 121 given 6=5 Critical Z value for gson is 1.96 2= 1.96 * Th + 2 * n = 1096 *5 * 2 * 5 = 9.8 Vo = 908 aro = 4.9 = (4.92 n=124] Ans; n = 24