Question

Suppose the population standard deviation is σ = 5 , an SRS of n = 100 is obtained, and the confidence level is chosen to be 98%. The margin of error for estimating a mean μ is given by: 1.165. 0.1228. 1.228. 0.1165.

Answer 1

1.165.

Explanation:

We have that to find our
`\alpha` level, that is the subtraction of 1 by the confidence interval divided by 2. So:

`\alpha = (1-0.98)/(2) = 0.01`

Now, we have to find z in the Ztable as such z has a pvalue of
`1-\alpha`.

So it is z with a pvalue of
`1-0.01 = 0.99`, so
`z = 2.33`

Now, find the margin of error M as such

`M = z*(\sigma)/(√(n))`

In which
`\sigma` is the standard deviation of the population and n is the size of the sample.

In this problem, we have that:

`\sigma = 5, n = 100`. So

`M = z*(\sigma)/(√(n))`

`M = 2.33*(5)/(√(100)) = 1.165`

So the correct answer is:

1.165.