Warm-up
Ch. 7 Practice Test
In the late 1990’s the Bill and Melinda Gates Foundation
began funding an effort to encourage the breakup of large
schools into smaller schools. Why? It had been noticed that
smaller schools were more common among best-performing
schools than one would expect. In time many other
organizations and the U.S. Department of Education’s Smaller
Learning Communities Program supported the effort. Well
over a billion dollars was spent making schools smaller. Two
statisticians discovered that in one particular state 12% of the
top scoring schools were the smallest 3% BUT also 18% of the
lowest scoring schools were also the smallest.
Explain why small schools show up at both extremes.
7.3 E #35
7.3 E #40
Example 2
Drivers in the Northeast and Mid-Atlantic states had the
highest failure rate, 20%,on the GMAC Insurance National
Driver’s Test. (They also were the drivers most likely to
speed.) Describe the shape, center, and spread of the
sampling distribution of the proportion of drivers. Who would
fail the test in a random sample of 60 drivers from these
states. What are the reasonably likely proportions of drivers
who would fail the test?
Whiteboard Review
1. Five math teachers are asked how many pens they
are currently carrying, and the results are 1, 1, 1, 2, 2.
Random samples of size two are taken from this population
(without replacement). What is the median of the sampling
distribution of the median?
A. 1
B. 1.4
C. 1.5
D. 2
E. None of the Above
Question 2) Whiteboard Review
Two antidepressants are to be compared in the treatment of elderly
patients in a nursing home. Each patient has his or her own room, some
with spectacular views of the ocean. The experimental design is to
create homogenous blocks with respect to the window view. How
should randomization be used for a randomized block design?
A. Within each block, randomly pick half of the patients to receive
each antidepressant.
B. Randomly pick half of all patients to receive each antidepressant, but
then analyze the results separately by blocks.
C. Randomly choose which blocks will receive which antidepressant.
D. Randomly choose half the blocks to receive each antidepressant for a
given time period; then for the same time period switch the medication
in each block and compare the results.
E. For ethical reasons, allow patients to choose which medication they
prefer taking, but then randomly assign patients to blocks.
Question 3) Whiteboard Review
There are two games involving flipping a fair coin. In the first
game, you win a prize if you can throw between 45% and 55%
heads; in the second game, you win if you can throw more
than 60% heads. For each game, would you rather flip the
coin 30 times or 300 times?
A. 30 times for each game.
B. 300 times for each game
C. 30 times for the first game, 300 for the second
D. 300 times for the first game, 30 for the second
E. The outcomes of the game do not depend on the number
of flips.
Question 4) Whiteboard Review
Which of the following statements are true?
I. Both dotplots and stemplots can show symmetry, gaps,
clusters and outliers.
II. In histograms, relative areas correspond to relative
frequencies.
III. In histograms, frequencies can be determined from
relative heights.
A. II only B. I and II C. I and III D. II and III E. I, II and III
Question 5) Whiteboard Review
The scores on a standardized test are normally distributed
with mean 500 and standard deviation 110. In a randomly
selected group of 100 test-takers, what is the probability
that the mean test score is above 510?
A.
B.
C.
D.
E.
Less than 0.0001
0.1817
0.4638
0.5362
0.8183
Question 6) Whiteboard Review
Last Bonus Question
On an average day in 2004, about 246,000 vehicles traveled
east on the Santa Monica freeway in Los Angeles to the
Interchange with the San Diego freeway. Assume that
a randomly selected vehicle is equally likely to go straight
through the interchange, go south on the San Diego freeway,
or go north on the San Diego freeway.
a. What is the best estimate of the number of vehicles that
will go straight through the interchange on an average
day?
b. What numbers of vehicles are reasonably likely to go
straight through?
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Directions to Ch. 7 Review
Complete the Ch. 7 Review
The test is not until Monday March 5th
We will review the Multiple Choice today and the free
response next block
Next block we will start on Ch. 8
Have your notebooks ready
Vocabulary: sampling distribution, standard error, reasonably likely,
rare events, standard error of the mean, Central Limit Theorem
(6 for 2 pts each = 12 pts) Formulas: S.E. and S.E. of the mean ( 4pts)
Notes with Warm-ups: 7.1, 7.2, 7.1 and 7.2 Review, 7.3
( 4 for 21 pts each; 15 for notes and 6 for warm-up = 84 pts)
Mistakes from the last quiz
Human gestation (pregnancy) times have a mean of about 266 days,
with a standard deviation of about 16 days.
1. Suppose we look at the average gestation time for a sample of 100
women. If we imagined all the possible random samples of 100,
what would the distribution look like? Draw it below.
16
S.E. of themean
 1.6
100
2. Label the center and the two standard errors of the mean on either
side of the center in your distribution diagram above.
3 Conditions
Randomization – It didn’t say anywhere the police
randomly selected cars, but you had to mention why or
why not there was randomization.
10% - 80 cars is definitely less than 10% of all the cards on
the major highway.
Success/failure- 70% of 80 cars is 56 cars that should be
speeding which is more than 10. 30% of 80 is also
greater than 10. There is enough in the sample to have
more than 10 in each of the categories of speeding or
not speeding.
Answers to Multiple Choice
1) C 2) B 3) A 4) C 5) B