Question

Construct the indicated confidence interval for the population mean μ using the t-distribution. 1-α = 0.99, x with bar on top = 37.5, s = 3.8, n = 17

a-(35.35,39.65)

b-(35.13,39.87)

c-(34.83,40.17)

d-(34.81,40.19)

Answer 1

c )solution

Given that,

= 37.5

s =3.8

n = 17

Degrees of freedom = df = n - 1 = 17 - 1 = 16

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2  df = t0.005,16 =2.921 ( using student t table)6

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

=2.921 * (3.8 / 17) = 2.69

The 99% confidence interval estimate of the population mean is,

- E < < + E

37.5 - 2.69 < < 37.5+ 2.69

(34.81,40.19)