in a random sample of 100 COB students, 54 planned on going to graduate school. the Stat Tool 95% C.I. was (.44,.64) interpret this interval

Question

100 COB students, 54 planned on going to graduate school. the Stat Tool 95% C.I. was (.44,.64) interpret this interval

Answer 1

The purpose of doing a random sample is to estimate a true, unknown value.  In this case, the true parameter we wish to know is "the proportion of COB students that plan on going to graduate school."  

 

We will denote those true value (which is unknown), by p.

 

In this particular random sample, we got an estimated p of .54 (not the true value, it's estimated).

 

A 95% confidence interval tells you that if you repeatedly re-sample, there is a 95% chance that your interval will cover the true value p.  

 

It's not the probability that p is in your interval, since p is not a random variable.  It's the interval that is random.

 

 

J.T.

Answer 2

We are 95% confident the true proportion of students going to grad school is between 44% and 64%

 

We would expect 95% of the intervals constructed in the same way to contain the true proportion of students going to grad school.  Since the proportion exists before we try to estimate it, we have either captured it (p=1), or failed to capture it (p=0).  Over the long haul 95% of the intervals will capture the true proportion. There is only a chance of 0 or 1 associated with any given interval.