Question

Construct the indicated confidence interval for the population mean mu using the​ t-distribution. Assume the population is normally distributed.

C= 0.99 , X= 14.7 S = 4.0 , N= 9 ;

C= 0.98 , X= 12.6 S = .89 , N= 19

Answer 1

a.

sample size = n = 9

Degrees of freedom = df = n - 1 = 9 - 1 = 8

t_{$\alpha$/2,df} = 3.355

Margin of error = E = t_{$\alpha$/2,df}* (s /√n)

= 3.355 * (4.0 / √9)

= 4.5

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

$\bar x$- E < μ < $\bar x$ + E

14.7 - 4.5 < μ < 14.7 + 4.5

10.2 < μ < 19.2

(10.2 , 19.2)

b.

sample size = n = 19

Degrees of freedom = df = n - 1 = 19 - 1 = 18

t_{$\alpha$/2,df} = 2.552

Margin of error = E = t_{$\alpha$/2,df}* (s /√n)

= 2.552 * (0.89 / √19)

= 0.5

The 98% confidence interval estimate of the population mean is,

$\bar x$- E < μ < $\bar x$ + E

12.6 - 0.6 < μ < 12.6 + 0.6

12 < μ < 13.2

(12 , 13.2)