Question

# If n=27, ¯ x (x-bar)=46, and s=9, find the margin of error at a 95% confidence...

If n=27, ¯ x (x-bar)=46, and s=9, find the margin of error at a 95% confidence level (use at least two decimal places)

If n=19, ¯xx¯ (x-bar)=48, and s=6, find the margin of error at a 95% confidence level (use at least two decimal places)

If n=16, ¯xx¯ (x-bar)=48, and s=6, find the margin of error at a 99% confidence level (use at least three decimal places)

a)

Given,

degree of freedom = n - 1 = 27 - 1 = 26

alpha = 0.05

t(alpha/2,df) = t(0.05/2 , 26) = 2.055529 = 2.056

Margin of error = t*s/sqrt(n)

substitute values

= 2.056*9/sqrt(27)

= 3.56

b)

Given,

degree of freedom = n - 1 = 19 - 1 = 18

alpha = 0.05

t(alpha/2,df) = t(0.05/2 , 18) = 2.100922 = 2.101

Margin of error = t*s/sqrt(n)

substitute values

= 2.101*6/sqrt(19)

= 2.89

c)

Given,

degree of freedom = n - 1 = 16 - 1 = 15

alpha = 0.05

t(alpha/2,df) = t(0.05/2 , 15) = 2.131449 = 2.131

Margin of error = t*s/sqrt(n)

substitute values

= 2.131*6/sqrt(16)

= 3.20

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