Question

Construct the confidence interval for the population mean μ.

c = 0.98​, x = 9.3​, s = 0.5​, and n = 50

A 98​% confidence interval for μ is ( ____ , ____ ).

Answer 1

Solution :

Given that,

= 9.3

s = 0.5

n = 50

Degrees of freedom = df = n - 1 = 50 - 1 = 49

a ) At 98% confidence level the t is ,

= 1 - 98% = 1 - 0.98 = 0.02

  / 2 = 0.02 / 2 = 0.01

t _/2,df = t_0.01,49= 2.405

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

= 2.405 * (0.5 / 50) = 0.1701

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

- E < < + E

9.3- 0.1701 < < 9.3 + 0.1701

9.1299 < < 9.4701

(9.1299 , 9.4701)