Answer:
Step-by-step explanation:
The confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = sample mean of group 1
x2 = sample mean of group 2
s1 = sample standard deviation for data 1
s2 = sample standard deviation for data 2
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, the z score for confidence level of 95% is 1.96
From the information given,
x1 = 430
s1 = 120
n1 = 36
x2 = 460
s2 = 140
n2 = 49
x1 - x2 = 430 - 460 = - 30
z√(s1²/n1 + s2²/n2) = 1.96√(120²/36 + 140²/49) = 1.96√400 + 400)
= 55.44
The confidence interval is - 30 ± 55.44
