Qn. 2 Confidence Interval (C.I)
Confidence Interval (C.I) for the difference in means is the probability that the acceptable mean will lie between the ranges at a given level of confidence.
C.I = P [µ±Zα .σAV]
At 95% C.I, Zα = 1.96
Variance σ2 =(∑_((x-AV))▒2)/N ; ∑_((x-AV))▒2 = (17.66-12.028)2+ (16.88-12.08)2+ (17.99-12.08)2+ (17.11-12.08)2 + (16.31-12.08+ (17.55-12.08)2)2+ (10.38-12.08)2 +(5.38-12.08)2+(5.44-12.08)2 +(5.07-12.08)2+(4.52-12.08)2+ (4.75-12.08)2 +(5.31-12.08)2+ (18.18-12.08)2 + (17.89-12.08)2 σ2 = 529.76/15 = 35.3173, Standard deviation σ = √(2&(∑_((x-AV))▒2)/N) ; σ = √35.3173 = 5.943, then the standard error of mean (σAV) = (σ )/√N ; = (5.943 )/√15 = 1.5345
C.I = 12.028 ± (1.96* 1.5345)
= 12.028% ± 3.008%
C.I = 9.02% ≤
could vary by as much as 4%. Assumption of SD of 2% may be not be correct.
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0.000 7 63 106 55 74.7 1.245 9 70 135 90 98.3 1.638 11 85 135 70 96.8 1.613 [ IMAGE ] [ IMAGE ] Conclusion = = = =
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