Question

Two random samples were selected independently from populations having normal distributions. The statistics given below were extracted from the samples. Complete parts a through c.

x overbar 1 =40.1

x overbar 2=30.5

If σ1=σ2​,

s1=33​,

and

s2=22​,

and the sample sizes are

n 1=10

and

n 2n2equals=1010​,

construct a

99​%

confidence interval for the difference between the two population means.

The confidence interval is

≤μ1−μ2≤

Answer 1

Given : = 40.1 ,   = 30.5, s1 = 33 , s2 = 22, n1 = n2 = 10.

In general, (1-)% confidence interval for μ1−μ2 is obtained as foolow :

where t(/2 , n1+n2-2) = t(0.005, 18) = 2.87844  ( from the t tables )

and Sp = = 28.04461

Thus, 99% confidence interval for μ1−μ2 is :

( -26.5011955 , 45.7011955 )

Hope this answers your query!