Transcript AP Statistics

AP Statistics
Chapter 7 Test
Review Answers
Concept Question #1
• A survey conducted by an unnamed polling firm
stated on October 29th, that Barack Obama was
predicted to receive 49.8% of the vote on
election day. On the actual day of the election,
he received 50.97% of the vote.
– Part a: Which of these numbers is a statistic?
• ANS: 49.8%
– Part b: Which of these number is a parameter?
• ANS: 50.97%
– Part c: after answering part a & b above, write each
of the given numbers using the correct ‘symbol’.
• ANS: p = .5097 & 𝒑 = .498
Concept Question #2
• When we talk about the ‘variability’ of a
statistic, then we are focusing on what aspect
of a distribution?
– ANSWER: The spread of the distribution.
Concept Question #3
• When we talk about the amount of “bias” in a
statistic, then what aspect of the distribution
are we talking about?
– ANSWER: The center of the distribution
Concept Question #4
• MULTIPLE CHOICE: Which of the following is the
preferred characteristic of an estimate of a
parameter
–
–
–
–
–
A. A statistic with high variability and low bias
B. A statistic with high variability and high bias
C. A statistic with low variability and low bias
D. A statistic with low variability and high bias
E. It doesn’t matter how much bias or variability a
statistic contains
• ANSWER: C…. The less bias and variability… the better.
Concept Question #5
• If you wish to reduce the amount of variability
in a statistic that we hope to use to estimate a
parameter, then what is the best way to
accomplish this?
– ANSWER: INCREASE the sample size.
Concept Question #6
• Two polling companies come to Pulaski County
(pop. 65,000) with the hopes of completing a
survey of its residents. One company plans to
survey 2500 residents, and the other plans to
survey 3100 residents. Which of the sampling
distributions would have the smaller 𝑠𝑥 ?
– ANSWER: The survey with 3100 residents… the larger
sample size, DECREASES variability/spread, so it would
produce a SMALLER standard deviation (𝑠𝑥 )
Concept Question #7
• A survey in 2006 of 500 randomly selected Kentuckians
found that 74% of them rooted for the Wildcats, 21% of
them supported the Cards, and 5% of them supported
neither. Suppose that the actual percentage of Wildcat
supporters was 63%.
– Part a: The mean of 𝜇𝑝 of p would be?
• ANSWER: 𝝁𝒑 = 𝟎. 𝟔𝟑… recall that we always use the ‘actual’ value
for this mean.
– Part b: Is 63% a parameter or a statistic?
• ANSWER: parameter
– Part c: Which of the following numbers is unknown: 74% or
63%?
• ANSWER: Technically, only God knows the value of a parameter, so
63% is unknown.
Concept Question #8
• A survey in 2006 of 500 randomly selected Kentuckians
found that 74% of them rooted for the Wildcats, 21%
of them supported the Cards, and 5% of them
supported neither. Suppose that the actual percentage
of Wildcat supporters was 63%.
– Part a: What would the standard deviation (𝜎𝑝 ) be?
• ANSWER:
.𝟔𝟑(.𝟑𝟕)
𝟓𝟎𝟎
= 𝟎. 𝟎𝟐𝟏𝟔
– Part b: What condition must be met in order to complete
the calculation stated in part a?
• ANSWER: the 10% condition, which states “the population MUST
be at least 10 times greater than the sample”
• This is often written symbolically as: n ≤ 0.10 N or n ≤ 𝟏 𝟏𝟎 𝑵
Concept Question #9
• A member of our boy’s basketball team makes 70% of
his free throw shots. Due to the fact that this player is
a starter and will play many minutes in each game, he
will make exactly 100 free throw attempts by season’s
end. Assuming that each free throw is independent,
what is the probability that his number of made free
throws exceeds 70?
– ANSWER: 0.500
• WORK SHOWN BELOW:
– 70 out of 100 is .70 (70%)
– P(z >
𝟎.𝟕−𝟎.𝟕
.𝟕(.𝟑)
𝟏𝟎𝟎
) = P(z > 0), which is 0.500
Concept Question #10
• Part a: In simplistic language, state the main
idea of the Central Limit Theorem.
– As ‘n’ increases, the sampling distribution
becomes more ‘normal’ in nature.
• Part b: In simplistic language, state the main
idea of the Law of Large Numbers.
– As ‘n’ increases, the value of 𝒙 gets closer and
closer to the value of 𝝁.
Concept Question #11
• What is the ‘magic number’ that ensures that
a sampling distribution will be approximately
normal, even if the parent population is highly
skewed to the right?
– ANSWER: According to the Central Limit
Theorem, 30 is the ‘magic number’.
Extra Concept Question #12
• What EXACTLY is the condition that must be
met in order to conclude that a ‘normal
approximation’ can be made (i.e.:
distribution is normal)?
–ANSWER:
n·p ≥ 10 AND n·q ≥ 10
Extra Concept Question #13
• What is the formula for standardizing (find a zscore) for a proportion?
Z=
𝑝−𝑝
𝑝𝑞
𝑛