Question

To estimate the mean of a normal population whose standard deviation is 6, with a bound on the error of estimation equal to 1.2 and confidence level 99% requires a sample size of at least:

a.166b
b.167
c.13
d.None of these choices

Answer 1

a) 166

Explanation:

Explanation:-

Step 1:-

maximum Error of estimation (E) =1.2

we know that maximum Error of estimation

`E = (S.D )z\alpha )/(√(n) )`

cross multiplication we get ,

E(√n) =σ (zₐ)

Squaring on both sides, we get

`n =( (z_(\alpha )S.D )/(E) )^(2)`

Step 2:-

Population of standard deviation σ = 6

level of significance ∝ = 2.576 at 99% of confidence interval

By using formula

`n =( (z_(\alpha )S.D )/(E) )^(2)`

substitute all values in above equation

`n =((2.576 X6)/(1.2))^2`

on simplification , we get n = 165.8 ≅166

Conclusion:-

confidence level 99% requires a sample size of at least (n)=166