3. Baseball Players’ Salaries. We have access to data regarding the salaries of all professional
baseball players in 2019. That is, if we consider all professional baseball players in 2019 our
subjects of interest, then we have information on every individual in the population. In this
problem, we are going to examine how varying the sample size impacts the sampling distribution
of the sample mean. We will be using an applet called StatKey to complete this problem. Before
you work on this problem, please watch the Lecture video for MODULE 4, Part 3
to understand how to use the applet. Then, open a web browser on your computer and
going to the following website:
http://lock5stat.com/statkey/sampling_1_quant/sampling_1_quant.html
(i) Suppose we drew many samples of size n = 50 and calculated the sample mean for each of
these samples.
i. How would the mean of the sample means from samples of size n = 50 compare to the
mean of the sample means from samples of size n = 10? (Choose one)
• The mean of the sample means based on samples of n = 50 would be larger than
the mean of the sample means based on samples of size n = 10.
• The mean of the sample means based on samples of n = 50 would be smaller than
the mean of the sample means based on samples of size n = 10.
• The mean of the sample means based on samples of n = 50 would be about the
same as the mean of the sample means based on samples of size n = 10.
• There is not enough information to answer this question.
ii. How would the standard error of the sample means from samples of size n = 50 compare
to the standard error of the sample means from samples of size n = 10? (Choose one)
• The standard error of the sample means based on samples of n = 50 would be larger
than the standard error of the sample means based on samples of size n = 10.
• The standard error of the sample means based on samples of n = 50 would be
smaller than the standard error of the sample means based on samples of size
n = 10.
• The standard error of the sample means based on samples of n = 50 would be
about the same as the standard error of the sample means based on samples of size
n = 10.
• There is not enough information to answer this question.
