This exercise explores the distribution of sample mean for larger random samples taken from a population with a shape that is quite skewed (students' earnings).
a. Because our population mean is 3.776 and standard deviation is 6.503, the mean of all sample means for samples of any size should be _____; the standard deviation for samples of size 40 should be _____. (The units are thousands of dollars.)
b. Explain why the shape of the distribution of sample mean for random samples of size 40 should be somewhat right-skewed but less so than for samples of size 10.
c. Twenty random samples of size n + 40 have been taken from several hundred values of the variable Earned, and the sample mean has been calculated each time:
Use software to find the mean and standard deviation of the sample means (report them to the nearest tenth) and to produce a histogram.
d. Tell briefly how center, spread, and shape of the distribution of sample mean for the 20 random samples of size 40 discussed in part (c) compare to the theoretical mean, standard deviation, and shape, as discussed in parts (a) and (b).