Question

Find the minimum sample size n needed to estimate for the given values of​ c, ​, and E. c​, ​, and E Assume that a preliminary sample has at least 30 members.

Answer 1

Answer:

hello your question is incomplete below is the complete question

Find the minimum sample size n needed to estimate μ For the given values of​ c, σ​, and E. c=0.98​, σ=6.5​, and E=22 Assume that a preliminary sample has at least 30 members.

Answer : 48

Step-by-step explanation:

Given data:

E = 2.2,

std ( σ ) = 6.5

c ( level of confidence ) = 0.98

To find the minimum sample size

we have to first obtain the value of  $Z_{a/2}$  

note : a can be found using this relation :

( 1 - a ) = 0.98 ----- equation 1

a = 1 - 0.98 = 0.02

hence:  a/2 = 0.01

This means that P( Z ≤ z ) = 0.99  the value of z can be found using the table of standard normal distribution. from the table the value of z = 2.33

P( Z ≤ 2.33 ) = 0.99

To obtain the sample size n

$n = (\frac{std*z}{E} )^{2}$

n = $(\frac{6.5*2.33}{2.2} )^2$ =  (6.88409)^2

Therefore n ≈ 48