sampling and 8. Provide the reasoning for the relationship you observed between distribution of the means and sample size. We refer to the standard deviation of the sample means as "standard error of the mean (SE,)." 9. According to your data in Table 3, the standard error of the mean decreases (increases/decreases) as sample size increases. Fortunately, we don't need to sample a population 500 times to get the standard error of the mean. Statisticians have developed a formula that allows you to estimate the standard error of the mean based on a single sample's standard deviation and sample size. SD SEX = Jn Sample Mean: 46.2193 Sample Std. Deviation: 8.0186 You will now compare the standard deviation of 500 sample means to the standard error of the mean calculated using data from a single sample Mean of 500 Sample Means: 50.1137 using the formula above. Sid. Deviation of the Means. 5.3725 Transfer the values for "Standard Deviation of the Means" from Table 3 into the appropriate column of Table 4. Resample the population a single time at each sample size in the table. 10. Record the sample mean and sample standard deviation in the table below. Leave the last two columns empty for now. Table 4. Standard Error & 95% Confidence Intervals Sample Sample Sample Standard Error of the Mean (SE=) 68% of samples 95% of samples Size Mean Standard Using SEX Standard Deviation of should have a should have a Deviation equation the Means mean between mean between SD Vn (# 1 SEX) (+ 2 SEX) 4 48.0 11.3 9 16 25 100 400 11. Use the formula for standard error of the mean to calculate the SE for each sample based on the sample standard deviation and sample size. a. Compare and contrast the two standard errors for each sample size (determined by the standard deviation of 500 sample means and by using the formula)