Question

Eat your cereal: Boxes of cereal are labeled as containing 14 ounces. Following are the weights, in ounces, of a sample of 12 boxes. It is reasonable to assume that the population is approximately normal. 13.03 14.98 13.12 13.13 13.11 13.03 13.16 14.98 13.06 13.05 13.12 13.13 2. Sand data Part: 0/2 WS Part 1 of 2 (a) Construct a 95% confidence interval for the mean weight. Round the answers to at least three decimal places. A 95% confidence interval for the mean weight is <u<

Answer 1

13.03 14.98 13.12 13.13 13.11 13.03 13.16 14.98 13.06 13.05 13.12 13.13 (x-x)2 0.1429 2.4719 0.0829 0.0773 0.0888 0.1429 0.0615 2.4719 0.1211 0.1282 0.0829 0.0773 Σχ=160.9 I Σ(x-x)2=5.9496

Mean (u) ==* =160.9/12=13.408 Variance (s) F(x-7)2 n-1 5.9496 12-1 5.9496 11 =0.5409 Standard deviation (s) = variance = 70.5409 = 0.7355

95% confidence interval (C.I)for the mean weight:- Degrees of freedom =n-1 = 12-1 =11 C95%=0.95

Significance level (a) =1-C =1-0.95 =0.05 Critical (t) = 1/2.df=2.201 (using t-value table)

vn V12 Formula of 95% C.I =x Et* =13.408 + 2.201*0.7355 =13.408+2.201*0.2123 =13.408+0.4673 = (13.408+0.4673, 13.408 -0.4673) = (13.875, 12.941) Therefore, 95% of C.I for means weight is 12.941 <u<13.875