Margin of error

Question

If n=28, (x-bar)=46, and s=8, find the margin of error at a 98% confidence level.

Give your answer to two decimal places.

Answer 1

Take Degrees Of Freedom as (n − 1) or (28 − 1) equal to 27.

Here sample Standard Deviation is simply given as 8 rather

than calculated and sample Mean is likewise given as 46.

The approximate Standard Error Of The Mean is σ^{^}_x-bar

equal to 8/√28 or 4/√7.

With sample size n less than 30, go to a

t-Table For Probabilities Under The t-Distribution Curve

and take the critical t-score t_c at the intersection of df = 27

and Confidence Level 0.98 to gain t_c as 2.473.

A 98% Confidence Interval For The Mean is obtained from

Lower Limit = x-bar − t_cσ^{^}_x-bar or 46 − (2.473)(4/√7);

Upper Limit = x-bar + t_cσ^{^}_x-bar or 46 + (2.473)(4/√7).

The Margin Of Error For The Sample Mean is recognized

as ±(2.473)(4/√7) or ±3.738824567 equivalent to ±3.74.