the past 10 years. There has also been a corresponding
decrease in family size, perhaps due to an increase in
single-parent families.2.31 The mean falls above the median.
2.33 Mean 5 21.33; median 5 21.
2.35 If you multiple by 5, for example, the mean will go
from 4.83 to 24.15; the median and the mode will go
from 5 to 25.
2.37 These fit nicely with what the earlier exercises led me
to expect.
2.39 This is a computer question.
2.41 Range 5 16; variance 5 11.592; standard deviation 5
3.405.
2.43 The interval 5 9.908 to 27.892
2.45 The standard deviation remains at 2.23 regardless of
what constant you add or subtract.
2.47 The new values are 2.381 3.809 1.428 3.809 etc.
2.49 This asks that you create a graphic.
2.51 This asks that you create a graphic.
2.53 For Appendix Data Set the coefficient of variation for
GPA is 0.351.
2.55 The 10% trimmed mean would be 32.675.
2.57 This question asks that you draw a graphic.
2.59 This is an Internet search.
Chapter 3
3.1 (b) 2 3, 2 2, 2 2, 2 1, 2 1, 2 1, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3
(c) 2 1.84, 2 1.23, 2 1.23, 2 0.61, 2 0.61, 2 0.61, 0, 0,
0, 0, 0.61, 0.61, 0.61, 1.23, 1.23, 1.84
3.3 (a) 68% (b) 50% (c) 84%
3.5 z 5 (950 2 975) 15 52 1.67; only 4.75% of the time
would we expect a count as low as 950, given what we
know about the distribution. The two-tailed probability
would be .095.
3.7 The answers to parts (b) and (c) of Exercise 3.6 will be
equal when the two distributions have the same stan-
dard deviation.
3.9 (a) $2512.68 (b) $1342.00
3.11 Multiply the raw scores by 10 7 to raise the standard
deviation to 10, and then add 11.43 points to each new
score to bring the mean up to 80.
3.13 z 5 (600 2 489) 126 5 0.88. Therefore 81% of the
scores fall below this, so 600 represents the 81st per-
centile.
3.15 z 5 0.79, p 5 .7852; X 5 586.591
For seniors and nonenrolled college graduates, a GRE
score of 600 is at the 79th percentile, and a score of 587
would correspond to the 75th percentile.3.17 The 75th percentile for GPA is 3.04.
>>>3.19 There is no meaningful discrimination to be made
among those scoring below the mean, and therefore all
people who score in that range are given a Tscore of 50.
3.21 The post intervention weights are reasonably normal,
but the weight gain and percentage gain are far from
normal. However, we have a very small sample.
3.23 You would probably do reasonably well if you treated
these as if they were normally distributed, especially if
you trimmed your samples. The extreme salaries may
well be people who worked in industry for many years
before coming to teaching or to those who were never
promoted above the rank of assistant professor but
stayed at the school for many years.Chapter 4
4.1 (a) I set up the null hypothesis that last night’s game
was actually an NHL hockey game.
(b) On the basis of that hypothesis, I expected that
each team would earn somewhere between 0 and
6 points. I then looked at the actual points and
concluded that they were way out of line with
what I would expect if this were an NHL hockey
game. I therefore rejected the null hypothesis.
4.3 Concluding that I had been shortchanged when in fact I
had not.
4.5 The critical value would be that amount of change be-
low which I would decide that I had been shortchanged.
The rejection region would be all amounts of change
less than the critical value—that is, all amounts that
would lead to rejection of H 0.
4.7 z 5 (490 2 650) 50 52 3.2. The probability that a stu-
dent drawn at random from those properly admitted
would have a GRE score as low as 490 is .0007. I sus-
pect that the fact that his mother was a member of the
board of trustees played a role in his admission.
4.9 The distribution would drop away smoothly to the right
for the same reason that it always does—there are few
high-scoring people. It would drop away steeply to the
left because fewer of the borderline students would be
admitted (no matter how high the borderline is set).
4.11 M is called a test statistic.
4.13 The alternative hypothesis is that this student was sam-
pled from a population of students whose mean is not
equal to 650.
4.15 The word “distribution” refers to the set of values ob-
tained for any set of observations. The phrase “sampling
distribution” is reserved for the distribution of outcomes
(either theoretical or empirical) of a sample statistic.
4.17 (a) Research hypothesis: Children who attend kinder-
garten adjust to first grade faster than those who
do not. Null hypothesis: First grade adjustment
rates are equal for children who did and did not
attend kindergarten.>Answers 737