Question

/viewform?hr submission=Chclk4feKBIQ.

☆

- Lox

1 point

A random sample of 500 army recruits has a mean height

of 68 inches with a standard deviation of 2.5 inches. If a

95% confidence interval is constructed, with all the

conditions having been met, what is the margin of error?

a) 68

c) .22

b) 6.02

d).184

Answer 1

c) .22

Explanation:

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

`\alpha = (1-0.95)/(2) = 0.025`

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
`1-0.025 = 0.975`, so
`z = 1.96`

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 question:

`\sigma = 2.5, n = 500`

Then

`M = z*(\sigma)/(√(n))`

`M = 1.96*(2.5)/(√(500))`

`M = 0.22`