Question

(100 POINTS!!!) Find the minimum sample size n needed to estimate for the given values of​ c, o ​, and E.

c=0.95​, o=7.6 ​, and E=2. Assume that a preliminary sample has at least 30 members.
n=?

Answer 1

56

Explanation:

The sample size is given by :

`n = (z_{_{(\alpha)/(2) }} (\sigma )/(E))^2\\`

We have c = 0.95

⇒ 1 - α = 0.95

⇒ α = 1 - 0.95

⇒ α = 0.05

⇒

`(\alpha)/(2) = (0.05)/(2) \\\\(\alpha)/(2) = 0.025 \\`

By lookat at the table values,

`z_{_{(\alpha)/(2) }} = 1.96`

So the sample size n is

`n = (z_{_{(\alpha)/(2) }} (\sigma )/(E))^2\\\\=(1.96 * (7.6)/(2))^2 \\\\= ((14.896)/(2) )^2\\\\=(7.448)^2\\\\= 55.47`

n ≈ 56