sample mean

[jessi]

The population of incomes in a particular community is thought to be highly right-skewed with a mean equal to $36,789 and standard deviation equal to $2,490. Based on this, if a sample of size n=36 is selected the highest sample mean that we would expect to see would be approximately $38,034.

My teacher said this is true, but how do I get this answer?

 

[JohnM]

Hint:

The sample means will have:

1. a normal distribution with a mean equal to the population mean, and
2. a standard error equal to the population standard deviation divided by the square root of the sample size

Use the z-tables to figure out if 38,034 is about as high as you might expect the sample mean to get, if you took many, many samples of size 36 (probably around 3 standard errors above the sample mean....)

 

[quark]

Hi Jessi,

It's probably the 95th or 99th percentile of the sampling distribution of the mean. To get it you need to calculte the standard error of the mean first. Post here if you have further questions.