Standard Error
As you are seeing, the Central Limit Theorem tells us that as long as the sample size is large enough, the shape of the population doesn't really matter (doesn't affect our distribution of sample means). So how large does the sample size need to be? Well, if the population is close to normal, you can still assume normality in the distribution of sample means for fairly moderate sample sizes. With a more skewed population, you will need a larger sample size.
As long as the sampling distribution of the sample means is approximately normal, then our approximation of the p-value should be similar regardless of the population shape.
However, it is more problematic that we don't know the population standard deviation. We can use the sample standard deviation s to approximate the population standard deviation. Then we approximate the standard deviation of the sample means by 
. This approximation to the standard deviation of the sampling distribution is called the standard error or 
.
(m) Calculate the standard error for our class data. (Show your work.)
(n) Use the standard error to standardize the observed sample mean compared to the assumed population mean: (observation - mean)/standard error. [You will interpret this just like before, how many standard errors is the observed statistic from the hypothesized parameter value.] (Show your work.)
(o) Does this standardized statistic provide strong evidence against the null hypothesis? Explain.
