Problems are from:
Sullivan, Michael, III. 2008. Fundamentals of Statistics, 2nd edition. Prentice Hall

2.3 - 8 (also, should that be in one, two, or three dimensions)
20800/16 = 1300; if the dollar sign is viewed as a two dimensional object, the linear dimension should differ by a factor of 1300^.5 = 36, if the dolar sign is viewed as a three dimensional object, the linear dimension should differ by a factor of 1300^(1/3) = 10.91. However, the comparison in dollars is not appropriate: they should use inflation adjusted dollars, or debt per person as a fraction of average salary, or some such comparison.

3.1 - 52 (also calculate the midrange wherever you calculated the mean and median)
(0.76+0.94)/2 = 0.85; no, it is very sensitive toextreme values, including errors if they result in extreme values.

3.2 - 46
a - range = 75-30 = 45; population variance (sigma squared) employs division by n rather than (n-1); the sample variance (division by (n-1)) is s^2 = 177.78, the sample standard deviation is s = 13.33.
b - The data has all shifted, but the spread is not affected, hence the answers are the same.
c - Multiplying all the data by the same number multiplies the spread by that number. range = (1.05)(45) = 47.25, s^2 = (1.05^2)(177.78) = 196 (a factor of 1.05^2), s = (1.05)(13.33) = 14 (the population standard deviation also differs by a factor of 1.05)
d - range = 100-30 = 70, s^2 = 379.17, s = 19.47.

**First Test**

5.1 - 12
The "probabilities" do not sum to one.

5.5 - 50
(21!)/((9!)(12!)) = 293930

7.2 - 50
a - find .9938 in the body of the table and read 2.5 off the margins
b - subtract 1-.4404 = .5596 to get the area to the left, then look for .5596 in the body of the table to get 0.15 from the margins of the table.
c - 1-.8740 = 0.1260 is in the tails, hence 0.0630 is in each tail, subtract 1-0.0630 = 0.9370 to get the area to the left of b (which includes one tail), find 0.9370 in the body of the table to get 1.53 in the margins.

7.5 - 24
E[x} = np = (80)(.2) = 16, V[x] = np(1-p) = (80)(.2)(.8) = 12.8, ((80)(.2)(.8))^.5 = 3.58
a - form z = (15.5-16)/3.58 = -.14 and z = (14.5-16)/3.58 = -.42, from the table .4443-.3372 = .11
b - form z = (19.5-26)/3.58 = .98, get .8365 from the table, but you want the area to the right, so 1-.8365 = .16
c - form z = (9.5-26)/3.58 = -1.82, get .0344 from the table.
d - form z = (18.5-16)/3.58 = .70 and z = (11.5-16)/3.58 = -1.26, from the table .7580-.1038 = .65

**Second Test**

**Third Test**

4.1 - 26 (I selected this problem because of d, consider also subtracting a millimeter from all measurements (or just the tibia measurements))
a - I am not going to do this here
b - 0.9513 (I did tis with the statistical package on a claculator)
c - a strong positive association
d - Neither multiplying all the data of one variable by a constant, or adding a constant to all the data of one variable will change the coefficient of correlation.
42
Linear regression only checks for a linear association. in the scatter diagram, income is greatest in the latter working years.

4.2 - 10 (you should calculate x-bar, y-bar, s_x, s_y, and r)
b - I would calculate x-bar = 6.2, y-bar = 2.04, SSxx = 36.8, SSyy = .852, SSxy = 5.36, b1 = 5.36/36.8 = .1457, b0 = 2.04-(.1457)(6.2) = 1.1367, hence y-hat = 1.14 + .15x
20 (also convert to inches)
a - y-hat = 1.11 + 1.39x (from calculator)
b - It is certainly not appropriate to interpret the y-intercept, since we are not considering mice with no humerus. The slope gives the increase in sizr of the tibia per increase in the humerus.
c - 37.96-(1.11+(1.39)(26.11) = .56 (hence above average since positive)
d -
e - 1.11+(1.39)(25.31) = 36.29
If both measurements (humerus and tibia) were converted to inches, the correlation and slope would be the same, but the y-intercept would be different. If one measurement (e.g., the humerus) was converted to inches but the other (i.e., the tibia) was not converted, the correlation would remain the same, but the slope would change (with the dependent variable unchanged, the y-intercept would not change)

4.3 - 12
0.9513^2 = .905 ((r^2) = (r)^2)