A particular investment fund is comprised of more than 1000 companies world-wide that are considered to be socially responsible investments. The average return rate for the companies in this fund last year was 6.5% with a standard deviation of 1.7% and the distribution was normally distributed. Imagine that you randomly select 10 samples of size 25 companies from this fund and record the sample mean return rates from last year for these 10 samples. Below are the sample mean return rates.
X-bar 1 = 3.1%
X-bar 2 = 4.3%
X-bar 3 = 6.9%
X-bar 4 = 1.2%
X-bar 5 = 3.1%
X-bar 6 = 0.7%
X-bar 7 = 5.4%
X-bar 8 = 8.3%
X-bar 9 = 9.4%
X-bar 10 = 6.5%
a. What is the mean of the sample means for the 10 samples of size 25 that you took (the ones listed above)?
b. If you continued to take samples of size 25 until you had taken all possible samples of size 25 from this population, what would be the mean of the sample means for all of your samples? What would be the standard deviation (standard error) of these sample means?
c. If you had taken repeated samples of size 50 instead of size 25, how would the distribution of your sample means have compared to the distribution of sample means for samples of size 25? You need not do any calculations here, but just say how it would compare.
d. What accounts for your answer in part c?