Private Colleges:
Sample mean = 42.7
sample standard deviation = 6.91
n = 10
51.8 44.2 46.0 32.3 43.0
31.6 45.8 38.8 51.5 42.0
Public Colleges:
sample mean: 22.3
sample standard deviation: 4.53
n = 12
20.3 22.0 28.2 15.6 24.1 28.5
22.8 25.8 18.5 25.6 14.4 21.8
Standard Error = 3.895
Margin of Error = 7.634
Critical value = 1.96
Point Estimate = 20.4 (private - public)
Mean annual cost for private = 20400 more than the mean annual cost for public.
What is the degree of freedom?
and
what is the 95% confidence interval of the difference between the mean annual cost of attending private and public colleges?
The degree of freedom is 20, calculated as (10-1) + (12-1) = 20.
The 95% confidence interval can be calculated using the formula:
(point estimate) +/- (critical value) * (standard error)
Substituting the values given:
20.4 +/- 1.96 * 3.895
The upper bound is:
20.4 + 7.634 = 28.034
The lower bound is:
20.4 - 7.634 = 12.766
Therefore, the 95% confidence interval of the difference between the mean annual cost of attending private and public colleges is (12.766, 28.034).