Question

Please find the Lower AND Upper bound of the above number set:

36, 52, 60, 60, 62, 65, 65, 65, 70, 72, 74, 75, 75, 76, 76, 78, 79, 79, 80, 80, 82, 83, 84, 85, 88, 90, 90, 92, 95, 98, 99

(NOTE: The answer is not 36 nor 42 for low bound nor 81.37 nor 110 for the upper bound. These were incorrect answers.)

Answer 1

Answer: find the Lower AND Upper bound of the above number set:

36, 52, 60, 60, 62, 65, 65, 65, 70, 72, 74, 75, 75, 76, 76, 78, 79, 79, 80, 80, 82, 83, 84, 85, 88, 90, 90, 92, 95, 98, 99

Solution:

Mean, x̄ = Σx /n

Mean, x̄ = 2365 /31

Mean, x̄ = 76.2903

S.D, s = √Σ(xi - x̄)^2/n-1

s = √Σ(xi - 76.2903)^2/31-1

s = √5752.3871/30

S.D, s = 13.8472

You are not provided confidence interval, so we use 95% confidence interval.

At 95% confidence interval, α = 0.05

Z critical =Zα/2 = 1.96

the 95% confidence interval:

CI = x̄ ± Z critical * σ/√n

CI = 76.2903 ± 1.96 * 13.8472 / √31

CI = 76.2903 ± 4.8746

CI = (71.4157, 81.1649)

Therefore,

Lower bound = 71.42

Upper bound = 81.16

If we consider 90% confidence interval,

At 98% confidence interval, α = 0.10

Z critical =Zα/2 = 1.645

the 90% confidence interval:

CI = x̄ ± Z critical * σ/√n

CI = 76.2903 ± 1.645 * 13.8472 / √31

CI = 76.2903 ± 4.0912

CI = (72.1991, 80.3815)

Therefore,

Lower bound = 72.20

Upper bound = 80.38

If we consider 99% confidence interval,

At 99% confidence interval, α = 0.01

Z critical =Zα/2 = 2.5758

the 99% confidence interval:

CI = x̄ ± Z critical * σ/√n

CI = 76.2903 ± 2.5758 * 13.8472 / √31

CI = 76.2903 ± 6.4061

CI = (69.8842, 82.6964)

Therefore,

Lower bound = 69.88

Upper bound = 82.70

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