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

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Answer:

The margin of error for estimating a mean μ is 1.1625.

Step-by-step explanation:

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

[tex]\alpha = \frac{1-0.98}{2} = 0.01[/tex]

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

So it is z with a pvalue of [tex]1-0.01 = 0.99[/tex], so [tex]z = 2.325[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

So

[tex]M = 2.325*\frac{5}{\sqrt{100}} = 1.1625[/tex]

The margin of error for estimating a mean μ is 1.1625.

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