Find the length of the confidence interval given the following data&nbsp;&nbsp;S=3 n=275 confidence level 95 %

Given:Sample standard deviation (s)&nbsp;=3Sample size (n) &nbsp;=275Confidence level&nbsp;=95%&nbsp;Level of significance level&nbsp;(α)=100-95=5%α=0.05&nbsp;p-value=[1-(α2)]=&nbsp;[1-(0.052)]=&nbsp;0.975&nbsp;From standard normal table:Critical value z at 0.975 is 1.96&nbsp;Error margin&nbsp;={Zα2×[sn]×2}={1.96×[3275]×2}=&nbsp;0.354577341×2=&nbsp;0.7092&nbsp;Thus, the confidence interval is 0.7092

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Confidence intervals

Answered question

2022-03-31

Find the length of the confidence interval given the following data

S=3 n=275 confidence level 95 %

Answer & Explanation

user_27qwe

Skilled2022-05-13Added 375 answers

Given:

Sample standard deviation (s) $= 3$

Sample size (n) $= 275$

Confidence level $= 95 %$

Level of significance level $(α)$

$= 100 - 95$

$= 5 %$

$α = 0.05$

p-value

$= [1 - (\frac{α}{2})]$

$= [1 - (\frac{0.05}{2})]$

$= 0.975$

From standard normal table:

Critical value z at 0.975 is 1.96

Error margin

$= {Z \frac{α}{2} \times [\frac{s}{\sqrt{n}}] \times 2}$

$= {1.96 \times [\frac{3}{\sqrt{275}}] \times 2}$

$= 0.354577341 \times 2$

$= 0.7092$

Thus, the confidence interval is 0.7092

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