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If n=21, ¯x (x-bar)=47, and s=6, find the margin of error at a 98% confidence level

User Linksonder
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1 Answer

16 votes
16 votes

The margin of error formula is given by


T_c*\frac{s}{\sqrt[]{n}}

where T_c is the critical T-value for n=21 degrees of freedom and s is the standard deviation. Then, for n=21 and 98% confidence level, we have that


T_c=2.5176

Therefore, by substituting these values into the margin of error formula, we have


T_c*\frac{s}{\sqrt[]{n}}=2.5176*\frac{6}{\sqrt[]{21}}

which gives


T_c*\frac{s}{\sqrt[]{n}}=3.2963

Then, the margin of error is 3.2963 and the confidence interval for the given mean is:


43.7037\le\bar{x}\le50.2963

User UmeshR
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