- Description
MTH 216
QUANTITATIVE REASONING II
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MTH 216 Week 1 Checkpoint
Prerequisite Assignment: MyMathLab® Study Plan for Weekly Checkpoint.
- Click on the Quiz tab.
- Click External Content Launch to access MyMathLab®.
- Click Homework and Tests in MyMathLab® at the top-left of the screen.
- Click Week 1 Checkpoint.
Important Notes: You must earn at least 60% of the Mastery Points in the weekly MyMathLab® Study Plan, before you may start the Weekly Checkpoint.
It is highly recommended that you earn all Mastery Points in the Weekly MyMathLab® Study Plan Checkpoint. You have 1 attempt to complete the Weekly Checkpoints and do not have access to the Help me Solve This or View an Example features.
Decide whether the statement below makes sense (or is clearly true) or does not make sense (or is clearly false). Explain.
In my experimental study, I used a sample that was larger than the population.
Choose the correct answer below.
A.
No, the statement does not make sense. The sample size should always equal the population size.
B.
Yes, the statement makes sense. A sample is always larger than the population.
C.
No, the statement does not make sense. A sample is a subset of the population and cannot be larger than the population.
D.
Yes, the statement makes sense. A sample can be as large as desired.
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.
I wanted to test the effects of vitamin C on colds, so I gave the treatment group vitamin C and gave the control group vitamin D.
Choose the correct answer below.
A.
The statement does not make sense. The control group should only receive a placebo, not another treatment.
B.
The statement makes sense. The treatment and control groups are receiving different treatments.
C.
The statement does not make sense. The vitamin C should be given to the control group, not the treatment group.
D.
The statement makes sense. The experiment has both a control group and a treatment group.
Identify any potential sources of bias in the following study.
An exit poll designed to predict the winner of a local election uses interviews
with every
Republican nbsp
who
votes between 8 : 00
and 11 : 00
a.m.
What sources of bias, if any, might this study have?
A.
Selection bias only
B.
Participation bias only
C.
Both selection and participation bias
D.
There is probably no bias in the study.
Discuss the differences between the following questions, each of which could be the basis for a statistical study.
bullet
What percentage of Internet dates lead to marriage?
bullet
What percentage of marriages begin with Internet dates?
Choose the correct answer below.
A.
The questions are too different to compare.
B.
The questions have different populations.
C.
The percentage of marriages beginning with Internet dates would be an observation while the percentage of Internet dates that lead to marriage would be an experiment.
D.
The percentage of marriages beginning with Internet dates can be accurately measured while the percentage of Internet dates that lead to marriage cannot be accurately measured.
The stacked line chart shows the numbers of college degrees awarded to men and women over time.
19001920194019601980200001234567891011121314YearCollege graduates (hundred thousands)
19001920194019601980200020040060080010001,2001,400
A stacked line chart has its horizontal axis labeled “Year” from 1900 to 2000 in increments of 5 and its vertical axis labeled “College graduates (hundred thousands)” from 0 to 14 in increments of 1. The area between the bottom line and the horizontal axis is shaded blue; the area between the top line and bottom line is shaded pink. The data for the bottom line are approximated as follows: 1900, 0.25; 1910, 0.25; 1920, 0.5; 1930, 0.75; 1940, 1; 1950, 3.75; 1960, 3; 1970, 5.25; 1980, 6.5; 1990, 5.75; 2000, 5. The data for the top line are approximated as follows: 1900, 0.25; 1910, 0.5; 1920, 0.75; 1930, 1.25; 1940, 1.75; 1950, 4.5; 1960, 3.75; 1970, 9; 1980, 10.5; 1990, 11.25; 2000, 11.75.
A legend shows that the color blue represents “Men” and the color pink represents “Women.” MenWomen
- Estimate the numbers of college degrees awarded to men and to women (separately) in 1930 and in 1990.
The number of college degrees awarded to men in 1930 was
75 comma 000
.
The number of college degrees awarded to women in 1930 was
50,000
.
The number of college degrees awarded to men in 1990 was
569,500
.
The number of college degrees awarded to women in 1990 was
548,500
.
- Compare the numbers of degrees awarded to men and to women (separately) in 1980 and 2000. Choose the correct answer below.
A.
In 1980, more men than women received degrees; in 2000, more women than men received degrees.
B.
In 1980 and in 2000, the number of men and women who received degrees were the same.
C.
In 1980, more women than men received degrees; in 2000, more men than women received degrees.
- During what decade did the total number of degrees awarded increase the most?
A.
1990s
B.
1940s
C.
1920s
D.
1960s
Compare the total numbers of degrees awarded in 1950 and 2000.
The total number of degrees awarded in 1950 was
445,000
.
The total number of degrees awarded in 2000 was
1,186,000
.
Consider the scatterplot to the right.
- State whether the diagram shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, is it strong or weak?
- Summarize any conclusions that can be drawn from the diagram.
Charitable Giving (11 States) as Percentage of Adjusted Gross Income (AGI)
$0$50,000$100,00000.511.522.533.54Average AGIPercent of AGI
A scatterplot with a horizontal axis labeled Average A G I from 0 to 100000 in increments of 20000 and a vertical axis labeled Percent of A G I from 0 to 4 in increments of 0.5 contains 11 points. The coordinates of the points are as follows: (41000, 1.25); (43000, 3); (45000, 2.5); (45000, 2); (48000, 1.5); (51000, 3); (59000, 1.25); (62000, 2.25); (70000, 2.5); (80000, 3.5); (82000, 1.75). All coordinates are approximate.
- Select the correct answer below.
A.
There is a strong positive correlation.
B.
There is a strong negative correlation.
C.
There is a weak negative correlation.
D.
There is a weak positive correlation.
E.
There is no correlation.
- Select the correct answer below.
A.
Higher AGI may imply slightly higher charitable giving as a percentage of AGI.
B.
Higher AGI implies much higher charitable giving as a percentage of AGI.
C.
Higher AGI may imply slightly lower charitable giving as a percentage of AGI.
D.
No conclusion can be drawn.
For the following pair of variables, state the units that might be used to measure each variable. Then state whether you believe that they are correlated. If you believe they are correlated, state whether the correlation is positive or negative. Explain your reasoning.
Altitude of aircraft and air pressure
To measure altitude
,
the unit
feet above sea level
might be used.
To measure air pressure
,
the unit
pounds per square inch
might be used.
What correlation, if any, is there between the variables?
A.
There is a positive
correlation because air pressure
tends
to increase when altitude
increases
B.
There is a negative
correlation because air pressure
tends
to increase when altitude
decreases
.
C.
The variables are not correlated.
For the following pair of variables, state the units that might be used to measure each variable. Then state whether you believe that the two variables are correlated. If you believe they are correlated, state whether the correlation is positive or negative. Explain your reasoning.
Altitude on a mountain hike and air pressure
To measure altitude
,
the unit
feet above sea level
might be used.
To measure air pressure
,
the unit
pounds per square inch
might be used.
What correlation, if any, is there between the variables?
A.
There is a negative
correlation because air pressure
tends
to increase when altitude
increases
.
B.
There is a positive correlation because air pressure tends to increase when altitude
decreases
.
C.
There is a positive
correlation because air pressure
tends
to increase when altitude
increases
.
D.
There is a negative
correlation because air pressure
tends
to increase when altitude
decreases
.
.
E.
The variables are not correlated.
The table to the right gives the per capita gross national product and the per capita expenditure on defense for eight developed countries. Gross domestic product (GDP) is a measure of the total economic output of a country in monetary terms. Per capita GDP is the GDP averaged over every person in the country. Complete parts a though c.
Country
Per Capita GDP ($)
Per Capita Defense ($)
A
36 comma 686
941
B
33 comma 153
824
C
34 comma 214
502
D
35 comma 430
1344
E
33 comma 929
329
F
47 comma 208
1225
G
35 comma 473
1006
H
45 comma 655
1729
- Make a scatter diagram for the data.
A.
200005500002000GDPDefense Spending
A scatterplot with a horizontal axis labeled G D P from 20000 to 55000 in increments of 5000 and a vertical axis labeled Defense Spending from 0 to 2000 in increments of 200 contains 8 points. (37500, 900); (32500, 800); (35000, 500); (35000, 1300); (35000, 300); (47500, 1200); (35000, 1000); (45000, 1700). All coordinates are approximate.
.
B.
200005500002000GDPDefense Spending
A scatterplot with a horizontal axis labeled G D P from 20000 to 55000 in increments of 5000 and a vertical axis labeled Defense Spending from 0 to 2000 in increments of 200 contains 8 points. (32500, 800); (32500, 650); (35000, 600); (35000, 1450); (35000, 100); (35000, 1400); (35000, 1000); (35000, 1700). All coordinates are approximate.
C.
200005500002000GDPDefense Spending
A scatterplot with a horizontal axis labeled G D P from 20000 to 55000 in increments of 5000 and a vertical axis labeled Defense Spending from 0 to 2000 in increments of 200 contains 8 points. (37500, 1100); (32500, 1200); (35000, 1500); (35000, 700); (35000, 1700); (47500, 800); (35000, 1000); (45000, 300). All coordinates are approximate.
D.
200005500002000GDPDefense Spending
A scatterplot with a horizontal axis labeled G D P from 20000 to 55000 in increments of 5000 and a vertical axis labeled Defense Spending from 0 to 2000 in increments of 200 contains 8 points. (37500, 1700); (32500, 500); (35000, 1000); (35000, 800); (35000, 900); (47500, 300); (35000, 1300); (45000, 1300). All coordinates are approximate.
- State whether the two variables appear to be correlated, and if so, state whether the correlation is positive, negative, strong, or weak.
A.
The two variables appear to be correlated and the correlation is strong and positive.
.
B.
The two variables appear to be correlated and the correlation is strong and negative.
C.
The two variables appear to be correlated and the correlation is weak and negative.
D.
The two variables appear to be correlated and the correlation is weak and positive.
E.
The two variables do not appear to be correlated.
- Suggest a reason for the correlation or lack of correlation.
A.
The higher a country’s per capita GDP, the more it can spend on per capita national defense.
B.
The higher a country’s per capita GDP, the less it can spend on per capita national defense.
C.
There is no correlation between a country’s per capita GDP and spending on per capita national defense.