Question

Calculate the margin of error

Eequals=z Subscript alpha divided by 2 Baseline times StartFraction sigma Over StartRoot n EndRoot EndFractionz?/2•?n

if the necessary requirements are satisfied.

The confidence level is

9090?%,

the sample size is

nequals=9292?,

and

sigma?equals=2020.

Answer 1

The margin of error is of 3.43.

Explanation:

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

`\alpha = (1-0.9)/(2) = 0.05`

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
`1-0.05 = 0.95`, so
`z = 1.645`

Now, find the margin of error M as such

`M = z*(\sigma)/(√(n))`

So

`M = 1.645*(20)/(√(92)) = 3.43`

The margin of error is of 3.43.

Answer 2

The margin of error is 3.465

Explanation:

Margin of error = t × sd/√n

n = 92, degree of freedom = n - 1 = 92 - 1 = 91, t-value corresponding to 91 degrees of freedom and 90% confidence level is 1.6618, sd = 20

Margin of error = 1.6618×20/√92 = 33.236/9.592 = 3.465