Standard Deviation Of P Hat

I just started my first statistics form and am not majoring in statistics so sorry if this sounds like a beginner question and also sorry if my language is incorrect. (experience free to correct me.) I take been learning about creating sample distributions of phat and also sample distributions of xbar. I was wondering if y'all 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 take two examples from my class 1 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 client 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 mean solar day period is more than five degrees above normal. Daily high temperatures in July are normally distributed with a mean of 84 degrees and a standard departure of viii degrees.

If we consider the first 16 days of July to be a random sample, what are the expected value, standard divergence, and shape of the sampling distribution of the sample mean? (don't answer this question it'due south just hither to prove the question in context.)

And now the second using the sample distribution of phat

Presume that 30% of all business students at a university invest in the stock market. We randomly pick 500 students

Prove the sampling distribution of phat, the sample proportion of concern students at this academy who invest in the stock market. (Yet once again no need to do this just giving context.)

So all the same once more I'm just request if in that location is a way to tell if I need to use the equations for xbar or for phat when given a mean, standard departure, and sample size and asked to give a sampling distribution. (And yes I know the second example says requite the sampling distribution of p-hat, just I desire to know if there is a way to tell if information technology didn't say that.) Thanks and lamentable over again if this is a bad question.

Here are the meanings of x bar and p lid that were used to solved the first and last question respectively:

Standard Deviation Of P Hat,

Source: https://stats.stackexchange.com/questions/87524/when-is-a-sample-proportion-p-hat-instead-of-x-bar

Posted by: dustinhatiltas.blogspot.com

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