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Suppose n=36,¯x=42n=36,x¯=42 and σ=14.9σ=14.9. Based on this, what is the maximal margin of error associated with...

Suppose n=36,¯x=42n=36,x¯=42 and σ=14.9σ=14.9. Based on this, what is the maximal margin of error associated with a 99% confidence interval for the true population mean.

Margin of error = Round to 2 decimal places.

Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that,

Point estimate = sample mean = = 42

Population standard deviation =    = 14.9

Sample size = n = 36

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576


Margin of error = E = Z/2 * ( /n)

= 2.576 * ( 14.9 /  36 )

= 6.40

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