Question

For the historical period 1926-2015, here are the sample statistics for the inflation-adjusted total returns on investment grade corporate bonds:

• sample size: n = 90
• x_mean = 3.38%
• s = 9.50%

Construct the one-sample t-confidence interval for a 0.95 level confidence interval for the population mean return.

Group of answer choices

(0.74%, 6.02%)

(-6.12%, 12.88%)

(1.72%, 5.04%)

(0.00%, 9.50%)

(1.39%, 5.37%)

Answer 1

Solution :

degrees of freedom = n - 1 = 90 - 1 = 89

t/2,df = t_0.025,89 = 1.987

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

= 1.987 * (9.50% / 90 )

Margin of error = E = 1.99%

The 95% confidence interval estimate of the population mean is,

  ± E

= 3.38% ± 1.99%

= ( 1.39%, 5.37% )