Answer:
Step-by-step explanation:
The formula for determining 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 sample 1
x2 = sample mean of sample 2
s1 = sample standard deviation for sample 1
s2 = sample standard deviation for sample 2
n1 = number of samples in sample 1
n2 = number of samples in sample 2
From the information given,
x1 = 934.1
s1 = 120.52
x2 = 1302.2
s2 = 178.6
For a 98% confidence interval, we would determine the z score from the t distribution table because the number of samples are small
Degree of freedom =
(n1 - 1) + (n2 - 1) = (10 - 1) + (10 - 1) = 18
z = 2.552
x1 - x2 = 934.1 - 1302.2 = -368.1
√(s1²/n1 + s2²/n2) = √(120.52²/10 + 178.6²/10) = √(1452.50704 + 3189.796)
= 68.13
Margin of error = 2.552 × 68.13 = 173.87
Therefore, confidence interval =
-368.1 ± 173.87
