Transcript File

JEOPARDY!
Click Once to Begin
FULL YEAR AP STATISTICS
REVIEW
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
JEOPARDY!
I, II, III…
GO!
PRO BA
BIL ITY!
Keenan’s
TOP
PICKS
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INFER
ENCE.
2002 AP
EXAM
Let’s Get
A 5!
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
INFERENCE 74
Which of the following are true?
I. The power of a test concerns it’s ability to
correctly reject a false Null Hypothesis.
II. The significance level of a test is the probability
of rejecting a true Null Hypothesis.
III. The probability of a Type I error plus the
probability of a Type II error is always equal to 1.
(A) I and II
(B) I and III
(C) II and III
(D) I, II, and III
(E) None are true.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(A) I and II.
I is the definition of power, II
is a Type I error, or alpha. III
is false.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
EXPERIMENTAL DESIGN 29
Which of the following are true statements about sampling?
I. Careful analysis of a given sample will indicate whether or
not it is random.
II. Sampling error implies an error, possibly very small, but still
an error, on the part of the surveyor.
III. Data obtained when conducting a census are always more
accurate than data obtained from a sample, no matter how
careful the design of the sample study.
(A) I only
(B) II only
(C) III only
(D) None of the statements are true
(E) None of the above gives the complete set of true
responses
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(D) To determine if a sample is random,
one must analyze the procedure by which
it was obtained. Sampling error is natural
variation, not an actual error. If a census
is poorly run, it will actually provide less
accurate information than a welldesigned survey. For example, having the
principal ask every single student
whether or not he or she regularly cheats
on exams produces less useful data than
a carefully worded anonymous
questionnaire filled out by a randomly
selected sample of the student body.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
INFERENCE 89
If all other variables remain constant, which of
the following will increase the power of a
hypothesis test?
I. Increasing the sample size
II. Increasing the significance level
III. Increasing the probability of a Type II error
(A) I only
(B) II only
(C) III only
(D) I and II
(E) All are true
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(D) I and II
Increasing the sample size WILL
increase power. Increasing the
significance level is the same as
increasing alpha (Type I error)
which also increases power.
Increasing the probability of a
Type II error will actually decrease
power.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
EXPERIMENTAL DESIGN 35
Consider the following three events:
I. Although 75% of Cubs fans believe they will go to the World
Series this year, in a random sample of 50 Cubs fans, only 30
“believe”
II. In a survey about literacy, an embarrassed adult deliberately
lies
III. A surveyor mistakenly records answers to one question in
the wrong space.
Which of the following correctly characterizes the above?
(A) I – sampling error, II – response bias, III – human mistake
(B) I – sampling error, II – nonresponse bias, III – hidden error
(C) I – hidden bias, II – voluntary bias, III – sampling error
(D) I – undercoverage error, II – voluntary error, III –
unintentional error
(E) I – small sample, II – deliberate error, III – mistaken error
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(A) I – sampling error, II –
response bias, III – human
mistake
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
DATA ANALYSIS 75
Which of the following are true statements?
I. If a sample has variance zero, the variance of the
population is also zero.
II. If the population has variance zero, the variance
of the sample is also zero.
III. If the sample has variance zero, the sample mean
and the sample median are equal.
(A) I and II
(B) I and III
(C) II and III
(D) I, II, and III
(E) None of the above gives the complete set of true
responses.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(C) II and III
If the variance of a set is zero, all the
values in the set are equal. If all the
values in the population are equal, the
same holds true for any sample of that
population. However, if all the values
of a sample are the same, that doesn’t
necessarily hold true for the whole
population. If all the values in a set are
equal, then the mean and the median
both equal this common value and
thus equal each other.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
PROBABILITY 46
Suppose 56 percent of 8 to 12 year olds
expect to have a “great life.” In an SRS of
125 eight to twelve year olds, what is the
probability that between 50 percent and 60
percent will say they expect to have a “great
life”?
(A) .2721
(B) .5402
(C) .6723
(D) .7279
(E) .8640
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(D) .7279
The sampling distribution of
p-hat has mean .56 and
standard deviation
[sqrt(pq/n)] = .0444. The
probability that lies between
.50 and .60 is .7279
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
PROBABILITY 63
For which of the following is a binomial an
appropriate model?
(A) The number of heads in ten tosses of an unfair
coin weighted so that heads comes up twice as
often as tails.
(B) The number of hits in five at-bats where the
probability of a hit is either .352 or .324 depending
upon whether the pitcher is left or right-handed
(C) The number of tosses of a fair coin before heads
appears on two consecutive tosses.
(D) The number of snowy days in a given week.
(E) The binomial is appropriate in all of the above.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(A) In choice B, p is not
constant. In choice C,
they’re asking about the
first success (two heads in
a row). In choice D, it is not
safe to assume
independence of a snow
day from one day to the
next.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
PROBABILITY 32
Given the probabilities Pr(A) = .3 and
Pr(A or B) = .7, what is the probability
Pr(B) if A and B are mutually
exclusive? If A and B are independent?
(A) .4, .3
(B) .4, 4/7
(C) 4/7, .4
(D) .7, 4/7
(E) .7, .3
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(B) If A and B are mutually
exclusive, then Pr(A) + Pr(B) =
Pr(A or B), thus Pr(B) = .4
If A and B are independent,
then Pr(A and B) = Pr(A)Pr(B).
Thus, by the General Addition
Rule, Pr(A or B) = Pr(A) + Pr(B)
– Pr(A and B) or .7 = .3 + Pr(B) .3Pr(B) yielding Pr(B) = 4/7
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
PROBABILITY 39
The Air Force receives 40 percent of its
parachutes from company C1 and the rest from
company C2. The probability that a parachute
will fail to open is .0025 or .002, depending on
whether it is from company C1 or C2,
respectively. If a randomly chosen parachute
fails to open, what is the probability that it is
from company C1?
(A) .0010
(B) .0022
(C) .4025
(D) .4545
(E) .5455
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(D) .4545
Create a tree diagram, set up
a conditional probability.
Pr(C1|fails) = Pr(BOTH) /
Pr(fails)
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
PROBABILITY 64
In a set of eight boxes, three boxes each contain
two red and two green marbles, while the remaining
boxes each contain three red and two green
marbles. A player randomly picks a box and then
randomly picks a marble from that box. She wins if
she ends up with a red marble. If she plays four
times, what is the probability she wins exactly
twice?
(A) .0606
(B) .3164
(C) .3221
(D) .3634
(E) .5625
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(D) .3634
The probability of winning is (3/8 x ½) +
(5/8 x 3/5) = 9/16, and the probability of
winning exactly twice in 4 games is
found using the binomial model for 2
successes in 4 trials, with a probability
of success at 9/16.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
INFERENCE 3
In general, how does doubling the
sample size change the confidence
interval size?
(A) Doubles the interval size
(B) Halves the interval size
(C) Multiplies the interval size by 1.414
(D) Divides the interval size by 1.414
(E) The question cannot be answered
without knowing the sample size
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(D) Increasing the
sample size by a
multiple of d divides
the interval by
sqrt(d)
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
PROBABILITY 58
The number of hybrid cars a dealer sells weekly has the
following probability distribution:
# of
hybrids
0
1
2
3
4
5
Pr(X=x)
.32
.28
.15
.11
.08
.06
The dealer purchases the cars for $21,000 and sells
them for $24,500. What is the expected weekly profit
from selling hybrid cars?
(A) $2,380
(B) $3,500
(C) $5,355
(D) $8,109
(E) $ 37,485
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(C) $5,355
The expected number of
cars sold per week is
1.53. Profit = 1.53($3,500)
= $5, 355
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
INFERENCE 69
A manufacturer of heart-lung machines periodically checks a
sample of its product and performs a major recalibration if
readings are sufficiently off target. Similarly, a rug factory
periodically checks the sizes of its throw rugs coming off an
assembly line and halts production if measurements are
sufficiently off target. In both situations, we have the null
hypothesis that the equipment is performing satisfactorily. For
each situation, which is the more serious concern?
(A) Machine producer: Type I error, carpet manufacturer: Type
I error
(B) Machine producer: Type I error, carpet manufacturer: Type
II error
(C) Machine producer: Type II error, carpet manufacturer: Type
I error
(D) Machine producer: Type II error, carpet manufacturer: Type
II error
(E) There is insufficient information to answer this question
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(C) In the production of heart-lung
machines, the more serious concern
would be a Type II error, which is
that the equipment is not performing
correctly, but the check does not
pick this up. As for the rugs, the
more serious concern would be a
Type I error, which is that the
equipment is performing just fine,
but the check causes them to halt
production.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
PROBABILITY 29
Suppose Pr(X) = .25 and Pr(Y) = .40.
If Pr(X|Y) = .20, what is Pr(Y|X)?
(A) .10
(B) .125
(C) .32
(D) .45
(E) .50
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(C) Pr(X and Y) =
Pr(Y)Pr(X|Y) =
(.20)(.40) = .08.
Then Pr(Y|X) = Pr(X
and Y) / Pr(X) =
.08/.25 = .32
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
PROBABILITY 62
Following are parts of the probability distributions for the
random variables X and Y.
X
Pr(X)
Y
Pr(Y)
1
?
1
.4
2
.2
2
?
3
.3
3
.1
4
?
If X and Y are independent and the joint probability Pr(X = 1, Y
= 2) = .1, what is Pr(X = 4)?
(A) .1
(B) .2
(C) .3
(D) .4
(E) .5
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(C) Pr(Y=2) = .5
By independence, Pr(X=1,
Y=2) = Pr(X=1)Pr(Y=2), and
so .1 = Pr(X=1)(.5) and
Pr(X=1) = .2.
Then Pr(X=4) = .3
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
INFERENCE 82
A high school has six math teachers and six
science teachers. When comparing their
mean years of service, which of the
following is most appropriate?
(A) A two-sample z-test of population means
(B) A two-sample t-test of population means
(C) A one-sample z-test for means
(D) A one-sample t-test for means
(E) None of the above are appropriate
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(E) With a
population of 12, we
will run no such
tests. CENSUS!
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
INFERENCE 30
A congressional representative serving on the Joint
Committee on Taxation states that the average
yearly charitable contributions for taxpayers is
$1,250. A lobbyist for a national church
organizations who believes that the real figure is
lower samples 12 families and comes up with a
mean of $1,092 and a standard deviation of $308.
Where is the p-value?
(A) Below .01
(B) Between .01 and .025
(C) Between .025 and .05
(D) Between .05 and .10
(E) Over .10
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(D) This is a lefttailed test with a tscore of -1.777 and a
p-value of .0516.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
INFERENCE 64
Which of the following are true statements?
I. The significance level of a test is the probability of
a Type II error.
II. Given a particular alternative, the power of a test
against that alternative is 1 minus the probability of
the Type II error associated with that alternative.
III. If the significance level remains fixed, increasing
the sample size will reduce the probability of a Type
II error.
(A) II only
(B) III only
(C) I and II
(D) I and III
(E) II and III
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(E) The significance
level is the
probability of a Type
I, not a Type II error.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
INFERENCE 62
There are 50,000 high school students in an extended
metropolitan region. As each of their students came in to
register for classes, guidance counselors were instructed to
use a calculator to pick a random number between 1 and 100.
If the number 50 was picked, the student was included in the
survey. For one of the may surveys, 30% of the students said
they couldn’t live without instant messaging. Are all
conditions met for constructing a confidence interval of the
true proportion of this region’s teens who believe they cannot
live without instant messaging?
(A) No, there is no guarantee that a representative random
sample is chosen.
(B) No, the sample size is not less than 10% of the population.
(C) No, np and nq are not both greater than 10.
(D) No, there is no reason to assume the population has a
normal distribution.
(E) Yes, all conditions are met, and a confidence interval can
be constructed.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(E) Sample is random, and there is
no reason to believe it is not
representative. Approximately 1 out
of every 100 students will be chosen
and 1% is clearly < 10% of the
population. Np = 150 and nq = 350
are both greater than 10. Nearly
normal is a condition for means, not
proportions.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
INFERENCE 111
Changing from a 95% confidence interval
estimate for a population proportion to a 99%
confidence interval estimate, with all other
things being equal,
(A) Increases the interval size by 4 percent.
(B) Decreases the interval size by 4 percent.
(C) Increases the interval size by 31 percent
(D) Decreases the interval size by 31 percent.
(E) This question cannot be answered without
knowing the sample size.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(C) The critical z will go
from 1.96 to 2.576, resulting
in an increase in the interval
size: 2.576/1.96 = 1.31, or an
increase of 31 percent.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
Suppose that 30 percent of the subscribers to a cable television
service watch the shopping channel at least once a week. You are to
design a simulation to estimate the probability that none of five
randomly selected subscribers watches the shopping channel at least
once a week. Which of the following assignments of the digits 0
through 9 would be appropriate for modeling an individual subscriber's
behavior in this simulation?
(A)
Assign "0, 1, 2" as watching the shopping channel at least
once a week and "3, 4, 5, 6, 7, 8, and 9"
as not watching,
(B)
Assign "0, 1, 2, 3" as watching the shopping channel at least
once a week and "4, 5, 6, 7, 8, and 9"
as not watching.
(C)
Assign "1, 2, 3, 4, 5" as watching the shopping channel at
least once a week and "6, 7 , 8, 9, and 0"
as not watching.
(D)
Assign "0" as watching the shopping channel at least once a
week and "1, 2, 3, 4, and 5" as not
watching; ignore digits "6, 7, 8, and 9,"
(E)
Assign "3" as watching the shopping channel at least once a
week and "0, 1, 2, 4, 5, 6, 7, 8, and 9"
as not watching.
Template by
Modified by
Bill Arcuri, WCSD
Chad Vance, CCISD
(A)
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
Which of the following statements is (are) true
about the t-distribution with k degrees of freedom?
I.
The t-distribution is symmetric.
II.
The t-distribution with k degrees of
freedom has a smaller variance than the
t-distribution with k + 1 degrees of
freedom.
III. The t-distribution has a larger variance
than the standard normal (z) distribution.
(A)
(B)
(C)
(D)
(E)
I only
II only
III only
I and II
I and III
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(E) I and III
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
As lab partners, Sally and Betty collected data for
a significance test. Both calculated the same
z-test statistic, but Sally found the results were
significant at the alpha = 0.05 level while Betty
found that the results were not. When checking
their results, the women found that the only
difference in their work was that Sally used a twosided test, while Betty used a one-sided test.
Which of the following could have been their test
statistic?
(A)
(B)
(C)
(D)
(E)
-1.990
-1.690
1.340
1.250
1.640
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(B) -1.690
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
Suppose that the distribution of a set of scores has a mean of 47
and a standard deviation of 14.
If 4 is added to each score, what will be the mean and the standard
deviation of the distribution of
new scores?
Mean
Standard Deviation
(A)
51
14
(B)
51
18
(C)
47
14
(D)
47
16
(E)
47
18
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(A)
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
The correlation between two scores X
and Y equals 0.8. If both the X scores
and the Y scores are converted to zscores, then the correlation between
the z-scores for X and the z-scores for
Y would be
(A)
(B)
(C)
(D)
(E)
-0.8
-0.2
0.0
0.2
0.8
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(E) .8
Converting to z-scores is a
combination of shifting and
scaling, neither of which
affects the correlation
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
DATA ANALYSIS
Consider the points (-1, 4), (2, 10), (4,
15), (7, 21), (10, n). What should n be
so that the correlation between the x
and y values is r = 1?
(A) 26
(B) 27
(C) 28
(D) A value different from any of the
above
(E) No value for n can make r = 1
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(E) Close observation
readily shows that the first
four points do not all lie on
the same line, and the only
way r = 1 is when all of the
points lie on the same line.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
EXPERIMENTAL DESIGN 24
Before taking an exam, students either went to bed
at their normal times or were sleep deprived for 4 or
8 hours. Half of each group were given a caffeine
pill before taking the exam. Determine the number
of factors, levels for each, and number of
treatments.
(A) One factor with two levels, five treatments
(B) Two factors, one with one and one with two
levels, three treatments
(C) Two factors, one with two and one with three
levels, five treatments
(D) Two factors, one with two and one with three
levels, six treatments
(E) Three factors, each with two levels, six
treatments
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(D) Two factors,
sleep deprivation
(three levels) and
caffeine (two levels),
with 3 x 2 = 6
treatments.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
INFERENCE 97
In the following table, what value of
n results in a table showing perfect
independence?
40
60
50
n
(A) 30 (B) 50
(E) 100
(C) 70
(D) 75
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(D) Relative
frequencies must be
equal throughout. 75
yields this result.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
PROBABILITY 31
The diastolic pressure among 20 to 30 year olds
is roughly normal. If 10 percent have levels
above 86 mmHg, and 20 percent have levels
below 69 mmHg, what is the mean of this
distribution?
(A) 74.7 mmHg
(B) 75.7 mmHg
(C) 77.5 mmHg
(D) 79.3 mmHg
(E) The mean cannot be calculated from the
given information
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(B) 75.7 mmHg
Create two
equations and solve
for the mean.
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
PROBABILITY 74
Suppose X and Y are independent random
variables, both with normal distributions. If X has a
mean of 30 and a standard deviation of 6, and Y has
mean 25 with standard deviation 4, what is the
probability that a randomly generated value of X is
greater than a randomly generated value of Y?
(A) .5000
(B) .6914
(C) .7440
(D) .7560
(E) .8413
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD
(D) We are looking for the Pr(X>Y) or the
Pr(X-Y>0).
X - Y has mean of 30 – 25 = 5 and
standard deviation (through the ADDING
of the variances) of 7.211.
Use normcdf to find Pr(X-Y>0) = .7560
Template by
Bill Arcuri, WCSD
Modified by
Chad Vance, CCISD