Question

What is the length of s=8.57, n=300, confidence level=95%

Answer 1

The length of the interval is of 1.8672.

Explanation:

Length of a confidence interval:

Margin of error multiplied by 2.

Confidence interval:

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 Z-table as such z has a p-value of
`1 - \alpha`.

That 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.

s=8.57, n=300

`\sigma = 8.25, n = 300`

Margin of error:

`M = z(\sigma)/(√(n))`

`M = 1.96(8.25)/(√(300))`

`M = 0.9336`

Length:

2*0.9336 = 1.8672

The length of the interval is of 1.8672.