In Table 7.4 on page 173, all ten top hitters in the major league baseball in 2011 had lower batting averages in 2012, supporting regression toward the mean. Treating averages as whole numbers (without decimal points) and subtracting their batting averages for 2012 from those for 2011 (so that positive difference scores support regression toward the mean), we have the following ten difference scores: 14, 39, 61, 60, 13, 21, 50, 93, 16, 61.
(a) Test the null hypothesis (that the hypothetical population mean difference equals zero for all sets of top ten hitters over the years) at the .05 level of significance.
(b) Find the p - value.
(c) Construct a 95% confidence interval.
(d) Calculate Cohen’s d.
(e) How might these findings be reported?
In Table 7.4