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

Question

asked Sep 12, 2022 155k views

1 Answer

MD Shahid Khan · Answer 1 · 2022-09-17T07:31:08+0000

Answer:

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.