Download Sampling Distributions

Exam 1 Review
Exam 1 Review
Top Incorrect Problems
• As you increase the number of observations in a sample
from 50 to 500, you are most likely to
a)
b)
c)
d)
leave the mean and standard deviation approximately unchanged.
make the shape of the distribution more skewed.
increase the standard deviation as the sample size increases.
decrease the standard deviation as the sample size increases.
• Why? The sample mean and sample standard deviation are
unbiased estimators of the population parameters.
01:830:200:10-13 Spring 2013
Exam 1 Review
Top Incorrect Problems
• If we know that the probability for z > 1.5 is .067, then we
can say that
a) the probability of exceeding the mean by more than 1.5
standard deviations is .067.
b) the probability of being more than 1.5 standard deviations away
from the mean is .134.
c) 86.6% of the scores are less than 1.5 standard deviations from
the mean.
d) all of the above
01:830:200:10-13 Spring 2013
Exam 1 Review
Top Incorrect Problems
• The population variance is
a)
b)
c)
d)
a biased estimate.
an estimate of the sample variance.
calculated exactly like the sample variance.
usually an unknown that we try to estimate.
• Why? The population variance is a constant. We usually try to
estimate the population variance using the sample variance.
01:830:200:10-13 Spring 2013
Exam 1 Review
Top Incorrect Problems
• In using ordinal data, which measure of central tendency
is probably least useful?
a)
b)
c)
d)
median
mode
You cannot use any measure of central tendency with ordinal data.
mean
• Why? Ordinal data do not represent evenly-sized intervals
(and are often not numerical), so means for ordinal data are
either undefined or they are meaningless. Ordinal data are
ranked, however, so locating the median or modal values is
straightforward and the resulting value is meaningful.
01:830:200:10-13 Spring 2013
Exam 1 Review
Top Incorrect Problems
• I am looking down on a parking lot in which 40% of the
vehicles are silver and about 25% of the vehicles are
pickup trucks. To estimate that probability that the next
vehicle to leave the parking lot will be a silver pickup, we
first need to
a)
b)
c)
d)
assume that the color and the type of vehicle are independent.
assume that the color and the type of vehicle are exhaustive.
assume that the color and the type of vehicle are mutually exclusive.
simply multiply the two probabilities.
• Multiplying the two probabilities together only gives you the
joint probability if the two events they represent (color and
type) are independent.
01:830:200:10-13 Spring 2013
Exam 1 Review
Sample Computational Problems
Use the frequency distribution table below to compute the mean
and median of the included data:
X
72
73
74
75
76
77
78
– median = 75, mean = 74.85
01:830:200:10-13 Spring 2013
f
3
0
6
4
4
1
2
Exam 1 Review
Sample Computational Problems
Compute the mean and standard deviation for the following
sample of data:
11, 14, 10, 7, 12, 3
• Solution:
– M = 9.5, s = 3.94
01:830:200:10-13 Spring 2013
Exam 1 Review
Sample Computational Problems
Mensa International is the most well-known of the high-IQ
societies, unusual clubs whose only criterion for entry is that
members score extremely well on an IQ test. To be considered
for membership in Mensa, applicants must score in the 98th
percentile on one of various IQ tests. For an IQ test normed to
have a mean of 100 and a standard deviation of 15, what is the
minimum score required for membership in Mensa?
• Solution:
– 130.75
01:830:200:10-13 Spring 2013
Exam 1 Review
Sample Computational Problems
Road tests of a certain compact car show a mean fuel
rating of 30 miles per gallon, with a standard deviation of 4
miles per gallon. What percentage of these cars will
achieve mpg ratings of
a) More than 35 miles per gallon
b) Less than 27 miles per gallon
c) Between 27 and 35 miles per gallon
Solutions:
a)
b)
c)
P(x>35) = 0.11
P(x<27) = 0.23
P(27<x<35) = 0.66
01:830:200:10-13 Spring 2013
Exam 1 Review
Top Incorrect Problems
• If we multiply a set of data by a constant, such as
converting feet to inches, we will
a) leave the mean unchanged but alter the standard deviation.
b) leave the mean and variance unaffected.
c) multiply the mean by the constant but leave the standard deviation
unchanged.
d) multiply the mean and the standard deviation by the constant.
01:830:200:10-13 Spring 2013
Exam 1 Review
Top Incorrect Problems
• A test score of 84 was transformed into a standard score
of –1.5. If the standard deviation of test scores was 4,
what is the mean of the test scores?
a)
b)
c)
d)
90
78
80
88
01:830:200:10-13 Spring 2013
Exam 1 Review
Top Incorrect Problems
• In a normal distribution, about how much of the
distribution lies within two (2) standard deviations of the
mean?
a)
b)
c)
d)
95% of the distribution
33% of the distribution
66% of the distribution
50% of the distribution
01:830:200:10-13 Spring 2013
Exam 1 Review
Top Incorrect Problems
• Which of the following is a good reason to convert data
to z scores?
a) We want to be able to estimate probabilities or proportions easily.
b) We think that it is easier for people to work with round numbers.
c) We want to make a skewed set of data into a normally distributed set of
data.
d) all of the above
01:830:200:10-13 Spring 2013
Exam 1 Review
Top Incorrect Problems
• When the distribution is symmetric, which of the
following are always equal?
a)
b)
c)
d)
median and mode
mean and mode
mean, median, and mode
mean and median
01:830:200:10-13 Spring 2013
Exam 1 Review
Sample Extra Credit Problem
In a certain population of interest, women have a mean
height of 65 inches, men have a mean height of 69 inches,
and both have a standard deviation of 2.75 inches. Assume
that men make up 46% of the population, with women
making up the remaining 54%. You randomly select a
person from this population:
a) What is the probability of selecting a person who is both a man and
taller than 67 inches?
b) What is the probability of selecting someone shorter than 67 inches
given that you select a woman?
c) What is the probability of selecting either a man that is taller than 67
inches or a woman that is shorter than 67 inches?
01:830:200:10-13 Spring 2013