For each of the following pairs of distributions first decid

For each of the following pairs of distributions, first decide whether their standard deviations are about the same or different. If their standard deviations are different, indicate which distribution should have the larger standard deviation. SAT scores for all graduating high school seniors (a_1) or all college freshmen (a_2) Ages of patients in a community hospital (b_1) or a children\'s hospital (b_2) Motor skill reaction times of professional baseball players (c_1) or college students (c_2) GPAs of students at some university as revealed by a random sample (d_1) or a census of the entire student body (d_2) Anxiety scores (on a scale from 0 to 50) of a random sample of college students taken from the senior class (e_1) or those who plan to attend an anxiety-reduction clinic (e_2) Annual incomes of recent college graduates (f_1) or of 20-year alumni (f_2) When not interrupted artificially, the duration of human pregnancies can be described, well assume, by a mean of 9 months (270 days) and a standard deviation of one-half month (15 days). Between what two times, in days, will a majority of babies arrive? A small minority of all babies will arrive sooner than A small minority of all babies will arrive later than In a paternity suit, the suspected father claims that since he was overseas during the entire 10 months prior to the baby\'s birth, he could not possibly be the father. Any comment?

Solution

I will answer all parts of 4.9 here . Please ask the rest questions seperately.

4.9

(a) Since not all graduating high school seniors go to college, thus the graduating high schools seniors must have more diversified set of people and hence a₁ will have higher standard deviation.

(b) In the community hospital patients of all ages can be admitted while in children\'s hospital only children can be admitted, thus the set b₁ has a higher standard deviation.

(c) Collge professionals is a bigger set in terms of diversity than the baseball players, thus c₂ will have a higher standard deviation than c₁.

(d) The census of whole body is a bigger set than students of a single university , hence the set d₂ will have higher standard deviation.

(e) All college students will consist of those who plan to attend an anti anxiety reduction clinis as well as those who do not intend to attend it too. Thus the set e₁ will have a higher standard deviation.

(f) Recent colllege graduates consists of only batch of graduates while the 20 year alumni batc consist of more than one batch. Thus teh set f₂ will have a higher standard deviation.