I'm trying to revise for an upcoming exam and have come across a past paper question for which I can't quite work out an answer. I can't find any reference in my lecturer's notes and can't quite figure out the best way to approach this problem.
Disclaimer: NOT Homework.
A supermarket sells bags of grapes which are priced according to an approximate weight of 500g. Each bag cannot weigh exactly 500g, and the supermarket admits to a standard deviation in the bag weights of approximatelv 5g around a mean of 500g.
The bag weights can be assumed to be normally distributed. To check that the claimed mean weight of 500g is not misleading, a consumer advocacy group took a sample of ten bags and weighed them.
The weights in grams of the bags were as follows:
500.2, 498.2, 486.3, 494, 502.9, 503.9, 487.9, 496.4, 483.7, 497.4
Define the bias of an estimator T of a population mean p, and show that the sample mean x̄ is an unbiased estimator for µ.
Any explanation or guidance would be greatly appreciated.
I eventually found a formula in the notes which seems like it might apply to this situation. However I am still unsure how to apply it in this situation :(
$$ bias(T) = E[T|\theta] − \theta. $$