I just started my first statistics class and am not majoring in statistics so sorry if this sounds like a beginner question and also sorry if my language is incorrect. (feel free to correct me.) I have been learning about creating sample distributions of phat and also sample distributions of xbar. I was wondering if you can tell the difference between when one is needed and when the other is needed by looking at a mean, standard deviation and sample size.
I have two examples from my class one requires a sample distribution of phat and the other a sample distribution of xbar
First example using the sample distribution of xbar
Aamco Heating and Cooling, Inc., advertises that any customer buying an air conditioner during the first 16 days of July will receive a 25 percent discount if the average high temperature for this 16 day period is more than 5 degrees above normal. Daily high temperatures in July are normally distributed with a mean of 84 degrees and a standard deviation of 8 degrees.
If we consider the first 16 days of July to be a random sample, what are the expected value, standard deviation, and shape of the sampling distribution of the sample mean? (don't answer this question it's just here to show the question in context.)
And now the second using the sample distribution of phat
Assume that 30% of all business students at a university invest in the stock market. We randomly pick 500 students
Show the sampling distribution of phat, the sample proportion of business students at this university who invest in the stock market. (Yet again no need to do this just giving context.)
So yet again I'm just asking if there is a way to tell if I need to use the equations for xbar or for phat when given a mean, standard deviation, and sample size and asked to give a sampling distribution. (And yes I know the second example says give the sampling distribution of p-hat, but I want to know if there is a way to tell if it didn't say that.) Thanks and sorry again if this is a bad question.