If is the inverse of
, then by definition of inverse functions,
Given , the inverse, if its exists, satisfies the equation above. Evaluate
at the inverse, we have
Solve for the inverse:
Given , we do the same thing as before to find its inverse.
Answer:
The expected participation rate is 0.637.
The standard error is 0.04397
Step-by-step explanation:
For each working age people asked, there are only two possible outcomes. Either they are in the labor force, or they are not. This means that we can solve this problem using binomial distribution probability concepts.
Binomial probability:
Expected value for the participation rate: The expected value is the probability of a success. In this problem, a success is a working age people being in the labor force. 63.7% of them are. So . This means that the expected participation rate is 0.637.
Standard error for the participation rate:
The standard error is given by the following formula:
.
In this problem, 120 people are asked, so
.
So the standard error is 0.04397