I have two problems.
One is asking for the parameter of interest, and the other the population of interest:
(1). A sales professional for Goetze Candy, the maker of Cow Tails, is told that the company currently averages $4 million in sales annually.
The company hires him to work as an outside consultant in order to increase their annual sales revenue.
After he has worked toward this goal for a year, they will conduct a hypothesis test to determine whether their sales revenue has actually increased.
(a). Define the parameter of interest.
(2). With the current equipment owned, a manufacturing plant is supposed to be able to produce 8 bottles of syrup every hour.
When the machine malfunctions, it sometimes begins going too fast, and then deformities occur.
Other times, it malfunctions by moving too slowly, also causing deformities to the product.
The machine's peak performance is maintained by keeping production as close to 8 bottles per hour as possible.
A quality control supervisor takes a random sample of hours and counts the number of bottles produced in order to test whether the machine is functioning correctly or whether it needs to be readjusted.
(a). Define the population parameter of interest.
For 1a is μ = the mean annual sales for Goetze Candy, but have no idea why, when does one know to use x-bar and when to use μ? They seem interchangeable at times.
For 2a is, μ = the mean number of bottles produced by this machine each hour, similar to above.
One asks for parameter of interest, the other the population of interest, both are μ, not sure why and why there is no x-bar.
Thank you
Simply put: The parameter is the number/object you wish to estimate, and the population is collection of individuals to which that parameter describes.
Parameters apply to populations. Statistics apply to samples. (Pro-tip: the appropriate items begin with the same letter!) So, a population mean, $\mu$ is a parameter. $\bar{x}$ is a statistic.
Hopefully this helps.