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

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1 vote

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.

User MD Shahid Khan
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