1
MATH 1280 Practice Milestone UNIT 1 Introduction
to Statistics (2020) – University of the People
Which of the following data types will be continuous?
•
Number of cars produced by a car company in a year
•
Numbe
...
1
MATH 1280 Practice Milestone UNIT 1 Introduction
to Statistics (2020) – University of the People
Which of the following data types will be continuous?
•
Number of cars produced by a car company in a year
•
Number of skyscrapers in a city
•
Number of correct answers on a ten-question true/false test
•
Weight of a baby whale
RATIONALE
For data to be continuous, it means it can take on any value inside of an interval. Since
the weight of a baby whale can take on any numerical value inside of possible ranges of
weights, it is continuous.
CONCEPT
Discrete vs. Continuous Data
2
Which of the following correctly identifies a sample with non-response
bias?
•
A person becomes ashamed to answer a question regarding his or her past drug use•
The wording of a question about politics causes the subject to misinterpret the meaning
of the question
•
A person selected to be a part of the survey is unable to be contacted or
refuses to participate
•
A telephone poll excludes individuals who do not have phones
RATIONALE
Non-response bias is simply when someone can't respond or refuses to do so.
CONCEPT
Nonresponse and Response Bias
3
One typical way to select a sample is to randomly pick phone numbers from a telephone
book.
Which of the following explains how the selection of the sample could be
biased?
•
The sample does not represent those that cannot afford a telephone.
•
All of these choices would introduce a bias.
•
The sample does not represent those that chose not to have a telephone.
•
The sample does not represent those do not list their phone numbers.
RATIONALE
By choosing to use a telephone number, they would be excluding anyone who might not
use a phone, doesn't want their number public, etc. By excluding these types of people,they would not capture all people in the population and if these groups would respond
differently in a study, the study would be biased.
CONCEPT
Bias
4
Max conducted a clinical trial for a new vitamin supplement. He had two groups in his
clinical trial. The control group was given a sugar pill, and the treatment group was
given the new vitamin supplement. However, many of the participants in the control
group reported improvements in their general health, similar to the treatment group.
The ________ may describe the reason some participants from the control
group reported health improvements.
•
response variable
•
placebo effect
•
confounding variable
•
treatment group
RATIONALE
When people in a control group indicate that there is some noticeable change, in this
case an improvement in health, this is an example of what we call a placebo effect.
CONCEPT
Placebo
5
In a survey of a large high school class, responses to which two of the
following questions will be qualitative?
•
What is your height in inches?•
Are you male or female?
•
Are you right-handed or left-handed?
•
How many minutes do you spend working on homework on a typical weeknight?
RATIONALE
Qualitative simply describes things and can't be represented with numbers which can
then be used in arithmetic. Gender simply describes someone.
CONCEPT
Qualitative and Quantitative Data
6
Which of the following describes cluster sampling?
•
Choose a sample in such a way that every nth person or item is included.
•
Choose a sample so that every member of the population has an equal chance of being
selected for the sample.
•
First divide the population into groups, and then randomly pick individuals from each
group, so that the sample is proportionate to the population.
•
Divide the population into groups, and then randomly select some groups.
Choose all the members within the selected groups to be part of the sample.
RATIONALE
Cluster sampling is when the population is broken up into clusters, which are generally
based on something like geography. You then randomly choose groups or clusters and
members of those clusters are included in the sample.
CONCEPTStratified Random and Cluster Sampling
7
A sample composed of people who are readily available or easily recruited
is called a __________ sample.
•
random
•
convenience
•
cluster
•
self-selected
RATIONALE
When you choose a sample based on how easy it is to gather the data, this is referred to
as a convenience sample.
CONCEPT
Convenience & Self-Selected Samples
8
A professional quarterback completed 66% of his passes in 2008 and 68% of his passes
in 2009.
Of the following choices, which of the following TWO are correct about the
quarterback’s completion rate?
•
It rose by 3%.
•
It rose by two percentage points.
•
It rose by 2%.•
It rose by three percentage points.
RATIONALE
We can note that the absolute difference between 2008 and 2009 is 66% to 68% or 2
percentage points.
To get the percent difference we take the absolute difference and divide by the initial
value:
So we can say the quarterback's completion rate rose by 3%.
CONCEPT
Using Percentages in Statistics
9
At a school of 1,500 students, 20% are left-handed. A student randomly selects 200
students and obtains 22% left-handed students. A second student takes another random
sample of 250 students and obtains 27% left-handed students.
Which of the following should the difference between the percentages be
attributed to?
•
The sample sizes were both too small, which is why they both obtained figures different
than 20%.
•
Random error; the numbers were different due to variability inherent in
sampling.
•
Both samples suffered from non-response bias.
•
The samples were not random samples.RATIONALE
When sampling from the population, even when you gather a random sample, there is
not a guarantee it will exactly equal the true population value. So, even in this case
where the sample values are not exactly equal to 20%, since the samples are randomly
drawn, this is probably simply due to the variability that occurs when sampling. This is
simply random error.
CONCEPT
Random and Systematic Errors
10
The following shows the Consumer Price Index (CPI) for the years 2000-2005. All of the
values use a reference year of 1983.
Which of the following is true about the CPI, based on the information?
•
$100 in 2000 would be equivalent to $178 in 2001.
•
$100 in 2004 would be equivalent to $189.70 in 1983.•
$100 in 1983 would be equivalent to $194.50 in 2005.
•
The CPI does not change very much from year to year.
RATIONALE
Recall that the CPI is a way to adjust for price level changes from year to year. The base
value for the CPI is 100 and all values are in reference to that value. Each CPI value for
a corresponding year tells us what the value of $100 in the base year is in the
corresponding year. So, the value of $100 in 1983 is equivalent to having $194.50 in
2005.
CONCEPT
Index Number and Reference Value
11
The type of experimental design that first divides participants into
homogeneous groups before randomly assigning treatments and controls is
called a(n) __________.
•
matched-pair design
•
randomized block design
•
multi-stage sampling
•
completely randomized design
RATIONALE
When we first break up items into block and then assign treatment, this is called a
randomized block design.
CONCEPT
Randomized Block Design12
Which of the following definitions corresponds with an observational
study?
•
Controlling the environment and observing the response
•
Measuring variables of interest but not attempting to influence responses
•
Selecting a sample from the population of all individuals about which information is
desired
•
Doing something intentionally to the individuals involved
RATIONALE
An observational study is one in which the researcher doesn't try and control for the
setting. They simply gather data on the variables in the study. An experiment is when
the researcher intentionally or actively controls for the setting in which the study takes
place.
CONCEPT
Observational Studies and Experiments
13
A poll was conducted two weeks before an election and showed that the incumbent
would win with 56% of the vote and a margin of error of 4%.
If the incumbent needs to receive at least half the votes to win the
election, can there be confidence in the incumbent’s victory?
•
Yes, because the lowest the incumbent could receive is 52% of the vote.
•
Yes, because the poll stated that the incumbent will win with 60% of the vote.•
No, because she could receive as low as 4% of the vote.
•
None of the above
RATIONALE
Recall for a confidence interval, we take the point estimate +/- margin of error. Using
this framework we take the point estimate of 56%, then add and subtract the margin of
error, 4%.
This gives us a CI of 52% to 56%.
Since the lower value is greater than 50%, we are confident that the incumbent should
earn at last 50% of the votes and win the election.
CONCEPT
Margin of Error
14
Jenae also noticed that some of the coffee labels were much more visually attractive
than others. She replaced the original coffee labels with plain white ones that had the
flavor printed in bold black letters, and she placed them on the coffee pots for a weeklong experiment.
Which of the following statements about Jenae's actions is FALSE?
•
By ensuring that the labels look the same, Jenae is controlling the "visual appearance"
variable.
•
Because all of her labels are the same, Jenae could replicate her experiment for other
companies.
•By making sure that the labels all look the same, Jenae is ignoring
randomization in her experiment.
RATIONALE
This is a description of an experiment. Jenae is controlling for things by using the same
labels. This allows for replication in other settings. By doing this, randomization is not
compromised.
CONCEPT
Experimental Design
15
Julie wanted to find out the approximate percentage of non-traditional female college
students at public universities. She decided to randomly select 25 females from each
university in her state and collect and analyze the data.
Select the statement that is TRUE.
•
The female college students at state universities are the sample, and the female college
students at all universities in the United States are the population.
•
All female college students at state universities are the sample, and the 25 females that
Julie interviews are the population.
•
The 25 females that Julie interviews are the sample, and all female college
students at state universities are the population.
•
The 25 females that Julie interviews are the sample, and the females that Julie does not
interview are the population.
RATIONALE
The population is the entire set of interest and the sample is a subset of that larger
group. In this case the 25 sampled women are the sample and the entire set of interest
is all females at all public colleges or universities in her state.
CONCEPTSampling
16
A binomial question is __________ an open question. A closed question
is __________ a binomial question.
•
always; sometimes
•
always; never
•
never; always
•
never; sometimes
RATIONALE
A binomial has only two responses. Since there are only two responses that can occur, it
is by definition a closed question and is not considered an open question. Closed
questions don't need to only have two responses. So, only closed questions with two
responses are binomial, but they could have more than two responses.
CONCEPT
Question Types
17
Which of these statements is true about a blind experiment?
•
The total population is divided into homogeneous blocks.
•
Some people involved are prevented from knowing certain information that
might lead to biased results.
•
Closely matched elements are paired and then treatments are allotted to them.•
The total population is divided roughly into some groups and then some of the groups
are randomly selected.
RATIONALE
Blinding helps to prevent members of a study know key information in order to prevent
them from behaving or responding in a fashion that would be biased if they knew if they
were in a treatment or control group. For example, if you knew you were in a treatment
group, you might be more inclined to say it is working or give responses that indicate
that it is.
CONCEPT
Blinding
18
Which of the following describes simple random sampling?
•
Choose a sample in such a way that every nth person or item is included.
•
Choose a sample so that every member of the population has an equal
chance of being selected for the sample.
•
First divide the population into groups, and then randomly pick individuals from each
group, so that the sample is proportionate to the population.
•
Divide the population into groups, and then randomly select some groups. Choose all
the members within the selected groups to be part of the sample.
RATIONALE
The definition of a simple random sample means that every item in the sample can be
chosen with equal probability.
CONCEPT
Simple Random and Systematic Random Sampling19
The type of experimental design where the assignment of experimental
units to treatment and control groups is random is called a(n)
__________.
•
matched-pair design
•
multi-stage sampling
•
completely randomized design
•
randomized block design
RATIONALE
When each element of a sample has an equal chance of being put into a treatment or
control group without considering any other factors, this is called a completely
randomized design. So each element in the sample has an equal chance of being put
into treatment or control.
CONCEPT
Completely Randomized Design
20
In a study to assess the risk of lung cancer with the number of cigarettes smoked per
week, researchers randomly selected subjects who smoked, collecting data on the
number of cigarettes they smoked per week, and made note of which subjects developed
lung cancer.
This is a(n) _________ statistical study.
•
prospective
•retrospective
•
experimental
•
survey
RATIONALE
Since they measured the number of cigarettes moving forward, this is called a
prospective study.
CONCEPT
Prospective and Retrospective Studies
21
Which of these random samples qualifies as a representative sample to find
out what parents think about the levels of college tuition fees in the state?
•
50 parents of college students from the state
•
50 residents of a county in the state
•
50 residents of a city in the state
•
50 parents of school students from another state
RATIONALE
For a sample to be representative it should look like and be drawn from the population
of interest. In order to understand how parents in the state think about tuition, they
should draw upon parents in the state who have children in college.
CONCEPT
Random & Probability Sampling
22The type of experimental design that groups experimental units based on
similar characteristics is called a(n) _________.
•
matched-pair design
•
randomized block design
•
multi-stage sampling
•
completely randomized design
RATIONALE
When you try and control for certain characteristics that might influence your findings
in a study by matching observations in pairs on those characteristics, it is an example of
matched-pair design.
CONCEPT
Matched-Pair Design
23
Consider the following dart board and darts.Using the words “accuracy” and “precision,” how would the arrangement of
darts be best classified if the thrower was aiming for the bullseye in the
center?
•
High accuracy and high precision
•
High accuracy and low precision
•
Low accuracy and low precision
•
Low accuracy and high precision
RATIONALEAccuracy refers to how well something performs. The darts are not near the center, so
they are not very accurate. Precision refers to how tightly packed the measures
are. Since the measures are close to one another, they are very precise.
CONCEPT
Accuracy and Precision in Measurements
24
Data that was gathered for a past study and re-used to answer questions in a
present study is called __________ data.
•
biased
•
raw
•
confounding
•
available
RATIONALE
Available data has already been collected. Since the data was gathered for a past study,
it is an available or existing dataset.
CONCEPT
Data
25
In the 2008 presidential primary, nearly every poll showed that Barack Obama would
win New Hampshire. The polls used random-digit dialers to call a random sample of
New Hampshire households. However, many college students came out in support of
Hillary Clinton, who ended up winning the primary.
Which of the following types of bias affected the conclusions the polls drew?
•
Response bias•
Deliberate bias
•
Non-response bias
•
Selection bias
RATIONALE
Selection bias refers to a mechanism where selection of the sample produces a sample
that is not representative. The use of random digit dialers will not capture people with
private numbers, don't have a phone, etc. So, using this selection mechanism might
produce a selection bias for the sample.
CONCEPT
Selection and Deliberate Bias
26
In measuring the mass of a 50-gram weight in a science class, some students use a
poorly calibrated balance and obtain a value of 55.5 grams.
The relative error in their calculation is ________.
•
-11%
•
9.9%
•
11%
•
-9.9%
RATIONALE
Recall that the percent error is equivalent to the absolute difference divided by the
actual value.If the absolute measure is 50 grams and the observed measure is 55.5 grams, then the
absolute error is:
So we calculate the percentage error to be:
CONCEPT
Absolute Change and Relative Change
27
The owner of an ice cream shop would like to determine statistically which age groups
(<13, 13-21, 22-35, 36-50, and >50) in his city prefer which flavors of ice cream, in order
to figure out how to stock the freezer cases at her store.
Which of the following would be the most appropriate study to obtain this
information?
•
Experiment
•
Observational study
•
None of the above
•
Census
•
Survey
RATIONALE
A survey would allow the owner to quickly gather information on customers and then
relate that back to the type of ice cream flavors they like.
CONCEPTSurveys
28
In experiments, a(n) _________ variable is controlled to explain a cause
and effect relationship.
•
dependent
•
explanatory
•
response
•
confounding
RATIONALE
When trying to understand how one variable affects another, the variable that influences
the outcome or response variable is called an explanatory variable. So changing the
explanatory variable helps us understand the response variable.
CONCEPT
Variables
29
A survey was conducted to find the number of hours that people spend on their phones
in a day. A group of 300 people in a shopping mall were asked about how long they
spend on their phone and It was found that 42 people spend at least two hours on their
phone in a day.
Which of these does not represent inferential statistics?
•
14% of the people surveyed in the shopping mall spend at least two hours on
their phone in a day.
•14% of the people who live in the county spend at least two hours on their phone in a
day.
•
14% of the people who visited the shopping mall spend at least two hours on their phone
in a day.
•
14% of the people who live in the city spend at least two hours on their phone in a day.
RATIONALE
Recall that an inference is when you take a sample, which is the data at-hand, and make
a larger conclusion about a group at-large. Simply stating 14% of the people in the
survey spend at least two hours on their phone doesn't draw a larger conclusion. It
simply describes what you found in the sample. So it is a descriptive statistic.
CONCEPT
Statistics Overview
[Show More]
 – University of the People.png)
 – University of the People.png)
 – University of the People.png)
.png)
