Mean wage per hour for all $5000$ employees working for a large company is $£15$ per hour with a standard deviation of $£4$. Let $x̅$ be the mean wage per hour for a random sample of employees selected from this company. Find the Mean and Standard Error of $x̅$ for a sample size of $25$ and $256$.
As $25$ is less than $30$, what does that mean? Do I have to go around the two numbers differently because one is above 30 and one is below? Thanks.
Comments: Let me guess: you've rushed to tackle the homework problems before studying the supporting text material or lecture notes. Please do the reading first. In particular, start by looking for the terminology and formulas in my first paragraph below and in @Henry's Comments.
It is safe to assume 5000 is "essentially infinite" compared with $n = 25.$ Then $\mu = £15$ and $E(\bar X) =\mu = £15$. Also, $\sigma = £4$ and $SD(\bar X) = \sigma/\sqrt{n} = £0.80.$ Then £0.80 is the standard error of the sample mean $\bar X.$
Because $n = 256 < \frac{1}{10}(5000)= 500,$ most authors would say it is OK to answer using the same method as for $n = 25.$ [Fussier authors would say that the 'finite population correction' should be used to find $SD(\bar X).$ You can google that, if it's not in your book.]
To reiterate @Henry's Comment, "30" has absolutely nothing to do with either part.