Question

Construct the indicated confidence interval for the population mean u using a​ t-distribution.

c=0.98​, x =112​, s=10​, n=15

The confidence interval is (_, _) ​(Round to the nearest tenth as​ needed.)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 112

sample standard deviation = s = 10

sample size = n = 15

Degrees of freedom = df = n - 1 = 15 - 1 = 14

At 98% confidence level the t is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

t _/2,df = t_0.01,14 = 2.624

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

= 2.624 * (10 / 15)

= 6.8

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

- E < < + E

112 - 6.8 < < 112 + 6.8

105.2 < < 118.8

The confidence interval is (105.2 , 118.8)