A total of 182 college students reported their actual weights and then answered the question, "What is your ideal weight?" The data were collected in the Fall semester of 1999.(Source: William Harkness, Pennsylvania State University) In the table below, we show the averages of the di fferences in actual and reported ideal weights for women and men, separately. Just to make it clear, the average woman considered herself to be about 10.7 lbs over her ideal weight, while the average man considered himself to be about 2.5 lbs over his ideal weight.
Women Men
Mean di fference 10.7 2.5
Standard deviation 11.3 13.8
Number of students 119 63
Use confidence intervals to determine whether or not (a) we can be 95% certain that the average woman considers herself overweight as compared to her ideal weight; and (b) whether or not the same is true of the men.