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 score of in-state applicants
x2 = sample mean score of out -of-state applicants
s1 = sample standard deviation for in-state applicants
s2 = sample standard deviation for out-of-state applicants
n1 = number of in-state applicants
n1 = number of out-of-state applicants
For a 90% 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) = (17 - 1) + (10 - 1) = 25
z = 1.708
x1 - x2 = 1046 - 1118 = - 72
Margin of error = z√(s1²/n1 + s2²/n2) = 1.708√(37²/17 + 50²/10) = 31.052239
Confidence interval is - 72 ± 31.052239
