Answer:
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean 1 (in-state applicants)
represent the sample mean 2 (out-of state applicants)
n1=35 represent the sample 1 size (in-state applicants)
n2=35 represent the sample 2 size (out-of state applicants)
sample standard deviation for sample 1 (in-state applicants)
sample standard deviation for sample 2 (out-of state applicants)
parameter of interest.
We are assuming that the population standard deviations are equal.
The confidence interval for the difference of means is given by the following formula:
(1)
Where
![s^2=\frac{(35 -1)20^2 +(35-1)25^2}{35 +35 -2}=512.5](https://tex.z-dn.net/?f=s%5E2%3D%5Cfrac%7B%2835%20-1%2920%5E2%20%2B%2835-1%2925%5E2%7D%7B35%20%2B35%20-2%7D%3D512.5)
![s=\sqrt{512.5}=22.638](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B512.5%7D%3D22.638)
The point of estimate for
is just given by:
In order to calculate the critical value
we need to find first the degrees of freedom, given by: