Question

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 =80.8, n=64, s=14.9, x̄ =80.8, n=64, s=14.9, 99% confidence

E=E=

Round to two decimal places if necessary

  <  μ  <  <  μ  <  

Round to two decimal places if necessary

b.  x̄ =32.3, n=45, s=18, x̄ =32.3, n=45, s=18, 90% confidence

E=E=

Round to two decimal places if necessary

  <  μ  <  <  μ  <  

Round to two decimal places if necessary

Answer 1

Ans:

a)n=64

df=64-1=63

critical t value=tinv(0.01,63)=2.656

Margin of error,E=2.656*(14.9/sqrt(64))=4.95

lower limit=80.8-4.95=75.85

upper limit=80.8+4.95=85.75

75.85 <  μ  < 85.75

b)n=45

df=45-1=44

critical t value=tinv(0.1,44)=1.680

Margin of error,E=1.680*(18/sqrt(45))=4.51

lower limit=32.3-4.51=27.79

upper limit=32.3+4.51=36.81

27.79 <  μ  < 36.81