Answer:
90% confidence interval for the difference between the two population means
( -23.4166 , -6.5834)
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given first sample size n₁ = 100
Given mean of the first sample x₁⁻ = 178
Standard deviation of the sample S₁ = 35
Given second sample size n₂= 100
Given mean of the second sample x₂⁻ = 193
Standard deviation of the sample S₂ = 37
<u><em>Step(ii):-</em></u>
Standard error of two population means
Degrees of freedom
ν = n₁ +n₂ -2 = 100 +100 -2 = 198
t₀.₁₀ = 1.6526
<u><em>Step(iii):-</em></u>
<u><em> 90% confidence interval for the difference between the two population means</em></u>
<u><em></em></u><u><em></em></u>
(178-193 - 1.6526 (5.093) , 178-193 + 1.6526 (5.093)
(-15-8.4166 , -15 + 8.4166)
( -23.4166 , -6.5834)