Question

A sample of 21 offshore oil-workers took part in a simulated escape exercise. The sample yielded an average escape time of 387.1 min. and standard deviation of 23 min. The 95% confidence interval for the true average of escape time is:

(A) (376.631    ,    397.569)
(B ) (377.263    ,    396.937)
(C) (378.444    ,    395.756)

Consider a population with population standard deviation σ=20. What is the minimum sample size required so that the margin of error of the 95% confidence interval of μ is not larger than 4?

(A) 97

(B) 96

(C) 25

(D) 98

*Multiple choice

Answer 1

1) The 95 % confidence interval for the true average of escape time

Xbar - t_{​​​​​​a/2} *( s/√n ) <   < Xbar + t_{​​​​​​a/2}*( s/√n)

For a = 0.05 , d.f = n -1 = 20

t_{​​​​​​a/2,n-1}= t_{​​​​​0.025 , 20} = 2.086

387.1 - 2.086*(23/√21) < < 387.1 + 2.086 *(23/√21)

376.631 < < 397.569

Option c is correct

2) Given = 20 , c = confidence level = 0.95

E = margin of error = 4

The required sample size n

n = ( Z_{​​​​​​a/2} * )² /E^{​​​​​​2}

For a = 0.05 , Z_{​​​​​​a/2} = Z_{​​​​​​0.025} = 1.96

n = (1.96*20)²/4²

n = 97