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

Solution :

Given that,

standard deviation = = 6

margin of error = E = 1.2

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Sample size = n = ((Z_/2 * ) / E)²

= ((2.576 * 6) / 1.2)²

= 165.8 = 166b

Sample size = 166b

option a) is correct