##### Question

In: Statistics and Probability

# Calculate the margin of error and construct the confidence interval for the population mean using the...

Calculate the margin of error and construct the confidence interval for the population mean using the Student's t-distribution (you may assume the population data is normally distributed).

T-Distribution Table

a.  x̄ =87.3, n=64, s=19.6, x̄ =87.3, n=64, s=19.6, 98% confidence

E=E=

Round to two decimal places

<  μ  <  <  μ  <

Round to two decimal places

b.  x̄ =31.6, n=44, s=14.6, x̄ =31.6, n=44, s=14.6, 90% confidence

E=E=

Round to two decimal places

<  μ  <  <  μ  <

Round to two decimal places

## Solutions

##### Expert Solution

Solution :

a) degrees of freedom = n - 1 = 64 - 1 = 63

t /2,df = t0.01,63 = 2.387

Margin of error = E = t /2,df * (s /n)

= 2.387 * ( 19.6 / 64)

Margin of error = E = 5.85

The 98% confidence interval estimate of the population mean is, - E < < + E

87.3 - 5.85 < < 87.3 + 5.85

( 81.45 < < 93.15 )

b) degrees of freedom = n - 1 = 44 - 1 = 43

t /2,df = t0.05,43 = 1.681

Margin of error = E = t /2,df * (s /n)

= 1.681 * ( 14.6 / 44)

Margin of error = E = 3.70

The 90% confidence interval estimate of the population mean is, - E < < + E

31.6 - 3.70 < < 31.6 + 3.70

( 27.90 < < 35.30 )

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