Math 150 exam 1 Review FA19
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Math 150 – Exam 1 Review
Name __________________________________________
Instructions:
Read each question carefully and provide a complete, clear, and concise explanation.
Remember,
communication in context is as important as all other content.
1.
You have calculated that the value of the standard deviation for a talk that you are giving as $50.03. What can
you conclude
2.
The New York Times conducted a poll on women's issues. The poll conducted telephone interviews with
1,497 adults randomly selected via random digit dialing from across the US. The poll omitted people without
telephones, and also left out Alaska and Hawaii to reduce cost. The omissions, mentioned in the description
above, were sources of bias.
What type of bias is this called?
3.
There is an increasing amount of pressure to ban texting while driving; in fact, about a dozen states have
imposed prohibitions and proposals for a national ban have been introduced in Congress. Even the wireless
industry reportedly supports state and local efforts to ban texting while driving. AAA recently released the
results of a survey to determine the proportion of US drivers that read or send text messages while driving.
The random telephone survey questioned U.S. residents 16 and older in April and May. In this situation, what
are the sample and the population?
4.
The developers of a new fertilizer designed to aid the growth of soybean plants want to determine how much
should be used to get the most benefit.
Forty soybean plants are randomly split into four groups of 10 plants.
Each group receives a different amount of fertilizer that is added to the plants’ daily water.
The amounts of
fertilizer are 0, 10, 20, and 30 grams per liter of water.
At the end of 3 weeks, the plants are cut at the soil line
and weighed.
Name the explanatory and response variables.
5.
A new startup company is looking to purchase a fleet of cars.
They trying to have the most consistent expense
sheet.
In order to achieve this, they have found the standard deviation for annual fuel cost for 4 different
types of sedans.
For simplicity, the cars are identified by color here.
Which car’s annual cost is the easiest to
plan for? In other words, which car will have the most consistent annual fuel expense, and how can you tell?
The following is the calculated standard deviations for each color: Red = $6620; Orange = $6877; Yellow =
$4340; Green = $5694
6.
Suppose a group of students who reported smoking marijuana was found to have lower test scores than a
group of students who reported they don’t smoke marijuana. What is the most that can be concluded with
regard to the population of all students?
1
7.
Most hotels use a survey to determine how they are doing.
This survey is given after a visit.
This survey
method could produce biased results for a number of reasons.
What are some obvious reasons?
8.
The annual profits of 5 large corporations in an area are given below.
Which number that describes the center
of a distribution should be used, mean, median, or mode, and why that one?
$135,000
$143,000
$163,000
$133,000
$1,213,000
9.
Apple claims 34% of everybody who owns a smartphone owns an iPhone.
You believe that this value is
much higher.
So you decide to do your own very informal study.
You decide to spend an entire Saturday
observing who has an iPhone and who doesn’t.
Besides the obvious biases involved with your “study”, you
have found that 43% of the people you observed owned an iPhone.
What is the parameter and what is the
statistic for this situation?
Namely, what is the difference between a parameter and a statistic?
10.
One hundred volunteers who suffer from severe depression are available for a study.
Fifty are selected at
random and are given a new drug that is thought to be particularly effective in treating severe depression. The
other fifty are given an existing drug for treating severe depression. A psychiatrist evaluates the symptoms of
all volunteers after four weeks in order to determine if there has been substantial improvement in the severity
of the depression. How would the organizers create this study to be double blind?
11.
A drug company wanted to test a new arthritis medication.
The researchers found 500 adults aged 25-35 and
randomly assigned them to two groups.
The first group received the new drug, while the second received a
placebo.
After one month of treatment, the percentage of each group whose arthritis symptoms decreased was
recorded and compared.
Who are the experimental units?
2
12.
Write one of the following sampling plan labels by the described plan:
Systematic
Cluster
Simple Random
Convenience
Stratified
I.
Everybody in an apartment complex is grouped by which floor they live on.
Then, two are invited from
each floor to participate in the sample.
II.
Everybody in an apartment complex is grouped by which floor they live on.
Specific floors are then
randomly selected.
Everybody who lives on those floors are then selected to be in the sample.
III.
The name of everybody living in an apartment complex is written on a separate card, the cards are placed
in a bag and three names are picked from the bag.
IV.
The name of everybody in an apartment complex is listed in alphabetical order.
The 12
th
person on that
list is randomly selected.
Next, every 4
th
person on the list is also selected for the sample.
V.
The first 60 people who walk into an apartment complex after 2pm on a Tuesday are select to be in the
sample.
13.
In a survey of 100 people who had recently purchased motorcycles, data on the following variables was
recorded. Circle the correct choice!
Weight of motorcycle as equipped at purchase
Categorical
Numerical Discrete
Numerical Continuous
Number of previous motorcycles owned by purchaser
Categorical
Numerical Discrete
Numerical Continuous
Number of years of marriage
Categorical
Numerical Discrete
Numerical Continuous
Telephone area code of purchaser
Categorical
Numerical Discrete
Numerical Continuous
Gender of purchaser
Categorical
Numerical Discrete
Numerical Continuous
Natural hair color of person who purchased the motorcycle
Categorical
Numerical Discrete
Numerical Continuous
3
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20.
The following table represents the number summaries for the profit obtained in resale of all houses in two
different markets: All values are in dollars.
Min
Q1
Median
Q3
Max
Mean
Std. Dev.
Market 1
1,765
12,897
23,786
45,678
69,861
34,821
1,725
Market 2
1,192
19,184
33,865
46,284
90,873
35,227
18,380
a.
What is the proper notation for the average and standard deviation for this situation?
b.
Based on the values of the mean and median, is the distribution for Market 2 likely to be approximately
symmetric, right skewed, or left skewed?
Why?
c.
You are the hired advisor for a company that buys houses, remodels them, and sells them for profit.
This
company is brand new and has very little money.
They are looking to begin their business in the safest market
(the one with the smallest risk). Which Market would you advise and why?
21.
Fifty volunteers who suffer from severe depression are available for a study. All are evaluated by a
psychiatrist for severity of symptoms on a ten-point scale prior to the study.
Twenty-five are assigned at
random and are given a new drug that is thought to be particularly effective in treating severe depression.
The
other 25 are given an existing drug for treating severe depression.
The same psychiatrist evaluates the
symptoms of depression of all volunteers on a ten-point scale after four weeks, recording the differences in
scores in order to determine if there has been substantial improvement in the severity of the depression.
Show
the flow chart for this experiment. (You must use the class guidelines.)
4
22.
The chemicals in clay used to make pottery can differ depending on the geographical region where the
clay originated.
Sometimes, archaeologists use a chemical analysis of clay to help identify where a piece of
pottery originated.
Such an analysis measures the amount of a chemical in the clay as a percent of the total
weight of the piece of pottery.
The table below summarize analyses done for three chemicals—X, Y, and Z—
on pieces of pottery that originated at one of the three sites: I, II, and III.
a.
For chemical Z, describe how the percentages found in the pieces of pottery are similar and how they
differ among the three sites.
b.
Suppose only one chemical could be analyzed in the piece of pottery.
Which chemical—X, Y, or Z—
would be the most useful in identifying the site where the piece of pottery originated? Justify your choice.
5
23.
AAA's Daily Fuel Gauge Report is updated daily and is the most comprehensive retail gasoline survey
available. Every day self-serve stations are surveyed and state average costs (including Washington D.C.), in
dollars per gallon, determined for 3 grades of gasoline and diesel.
The histogram below is the data of the state
average costs (including Washington D.C. for one of those fuel types is shown below.
(FYI, this data is from
2011!!)
Dollars per gallon
Number of States
3.8
3.6
3.4
3.2
3.0
2.8
2.6
20
15
10
5
0
Price of Gas
a)
What is the variable being measured?
b)
What are the class intervals?
c)
Use the histogram to describe the distribution of the variable in context using all class guidelines.
6
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24.
Researchers studying a pack of gray wolves in North America collected data on the length x, in
meters, from nose to tip of tail, and the weight y, in kilograms of the wolves.
A scatterplot of
weight versus length revealed a relationship between the two variables described a positive,
linear, and strong.
a.
For the situation described above, explain what is meant by each of the following words.
i.
Positive:
ii.
Linear:
iii.
Strong:
The data collected from the wolves were used to create the least-squares equation:
^
y
=
16.46
+
35.02
x
.
b.
Interpret the meaning of the slope of the least-squares regression line in context.
c.
Use the model to predict the weight of a wolf that is 1.6 meters in length.
d.
Why would we not use the model to predict the length of a wolf that is 25kg in weight?
7