Question

Question 8 a) Find 98% confidence intervals for the true population means given the following information: = 19.8 S 3.5 n 9 b) Coca-Cola has been producing their drink in 300 ml bottles. However, a suspicious Statistician has noticed that there is variation in the actual volume of the contents from bottle to bottle. The distribution of the contents is normal with standard deviation a 3 ml. The Statistician who suspects that Coca-Cola is under-filling the bottles, measures the contents of six bottles; which turn out to have the following amounts of fill: 299.4; 297.7; 301.0; 298.9; 300.2; and 297.0 ml ls this convincing evidence that the mean content of the bottles is less than the volume of 300 ml that appears on the label of the 300 ml bottle? Test at a 0.05 level of significance Find the p-value and state what it means.

Answer 1

[Page-I] Quesition. 8° a) To find 98 y for the true confidence intervcels population means Given : T = 19.8 S = 3.5 - nag formulce for confidence intervals given here o is not we use s. t=to.i,& table value. t'tg, o., = 3.355 table value Lower limit 80 tison 19.8 - 3.355

Page-2] =1918-3-355 x 35 -19.8 - 3.355 X 1.1667 - 19.0 - 3.914 =:15.886 lower limit = 15.886] upper limit F + ť s 19.8 + 3.355* 35 ل = 19.8 +3.914 = 23.714 upper limit - 23.714 ( 15.886, 23.714)

| Page. 3) Question of b) Given Gtandard deviction =6=37 5= 3 ml, n= 6 data 299.2, 297.7 301.0 298.9 300.2 297.0 No = 300 i) Hypothesis : Hoiu=lo vs H, : H< 2=x-lo NN(0,12) 615 * = 199412 2. 299.03 - 300 3156

page-4) = -0.97 3150 23-0.492 1 2 = -0.792 > - Zd=-1.64 iz 1 = 0.792 < 22=1.64 calculated value < table cable .. we accept Ho at 5% level of significance. 10) P-value = 0.21418 i Pavelee >0.05 .. we accept Ho at 5% level of significance. it mecens the content of the bottles is equal to the volume of 300 ml that appears on the lable of the 300 ml bottles.