When to use Z scores or t scores?

jessicaf

New Member
Hi everyone,

I have lots of trouble with Z scores and t scores........A lot of times we are given the standard deviation; however, the question doesnt specify whether the standard deviation is a sample one(that we need to use t scores) or a real one(that we need to use Z scores). Could anyone please tell me when to use Z scores and when to use t scores?

Thanks a lot!! =)

JohnM

TS Contributor
The rule of thumb is to use t when the sample size is below 30 and/or when the population standard deviation is unknown (estimated from sample data).

jessicaf

New Member
I encountered a weird problem that uses Z-scores even though the sample size is 6...please take a look at the following:

"Alex buys a 6-pack coke. Suppose the amount of coke in each can follows a normal distribution with mean = 12.06 oz and with SD = 0.15oz. Assume all cans are filled independently of each other. Find the probability that the first can of coke that Alex takes is underfilled, i.e. there's less than 12oz coke in the can"

The answer uses Z-scores instead of t-scores. Is using Z-scores better than using t-scores in this particular question? Thanks a lot!!!

JohnM

TS Contributor
In this case, the std dev is known - the way the second sentence is worded suggests that they are referring to the population of coke cans, not the sample of 6 that were purchased.