Question

Find the sample size required to achieve the given margin of error with SD = 51.02 and z - score = 1.96. Round your answer to the nearest whole number. margin of error = 2

Answer 1

The sample size required is 2500.

Explanation:

z-score:

In function of the margin of error M, the z-score is given by:

`Z = (M)/((\sigma)/(√(n))) = (M√(n))/(\sigma)`

In this question, we have that:

`\sigma = 51.02, M = 2, Z = 1.96`

So

`Z = (M√(n))/(\sigma)`

`1.96 = (2√(n))/(51.02)`

`2√(n) = 51.02*1.96`

`√(n) = (51.02*1.96)/(2)`

`(√(n))^2 = ((51.02*1.96)/(2))^2`

`n = 2500`

The sample size required is 2500.