Statistics / Mr. Hansen 9/29/2004

Name: ________________________

Answers to Recent Problems from Chapters 1 and 2

	Note: Odd-numbered answers are in the back of the book. Remember that all problems require supporting work. In the case of normal probability computations, a rough sketch with shading will suffice.
1.46	Yes; both IQR and s will increase by 5% (i.e., will be multiplied by 1.05). This is logical, since IQR and s both are in units of dollars (unlike variance, for example, which is in units of dollars squared).
1.52	Presumably you were able to generate the several types of graphs requested. Note that the textbook did not require all of those graphs, only the analysis. From the paired relative frequency bar graph (number 2 of the 3 types listed in the assignment), one can see that the younger age group had a significantly higher percentage that attended or completed college, and a significantly lower percentage that had only a high school education or less. Interestingly, though, the two age groups had nearly the same percentage with an advanced degree, from which we can conclude that the proportion of college-educated old-timers who earned an advanced degree was higher than the proportion of college-educated people age 25-34 who earned an advanced degree.
2.38(a)	Line segment from (0, 0) to (Ö2, Ö2).
(b)	Median = (point at which areas to left and right both equal .5) = 1 by techniques from Form III geometry. (A = ½bh for a triangle, A = ½(b1 + b2)h for a trapezoid. Coming from the left is easier, since you would use the triangle formula, and by the nature of the problem, b = h. Therefore, let x denote the common value of b and h. Solve the equation A = ½x^2 = .5 to find x, the median.)
	Q1 = .707 by applying triangle area formula. (Set area equal to .25 and solve.)
	Q3 = 1.225 by applying trapezoid area formula. (Set area equal to .25 and solve.) Or, you may find it somewhat easier to use the triangle formula, again approaching from the left. (Set area equal to .75 and solve.)
(c)	To the left, since the distribution is skew left. (Using calculus techniques, one can prove that m = 2^1.5/3 » .943, but doing that is beyond the scope of this course.)
(d)	12.5%, 0%
2.40	Joey outscored 97% of the students who took the reading test, but he outscored only 72% of the students who took the math test. Relative to the population of students who took the tests, Joey did better on reading than on math.
2.42(a)	z = 2.054
(b)	z = .772
2.44(a)	15.9%
(b)	.13%
(c)	2.28%
(d)	28.37
2.46	5.2%, 7.8%
2.48	3.42 or above, 2.58 or below
2.50	Both plots are fairly close to a “straight line” pattern, though of course your interpretation may differ. Transcribe the plot and state your opinion. Since a straight line on the NQP indicates normality, the use of the sample mean (xbar) and sample s.d. (s) to summarize the data would be justified.