Name: ________________________ Class: ___________________ Date: __________
ID: A
1
Advanced Math Pre/Post Test - Spring
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Decide if the following statement makes sense (or is clearly true) or does not make sense (or is clearly false).
The bank that pays the highest annual percentage rate (APR) is always the best deal
a.
The statement does not make sense because a higher APR always results in a lower
annual percentage yield than an interest rate with a lower APR
b. The statement does not make sense because, depending on how often the interest is
compounded, a lower APR could result in a higher annual percentage yield.
c.
THe statement makes sense because a higher APR always results in a higher annual
percentage yield than an interest rate with a lower APR.
2. Use the compound interest formula to compute the balance for the following account assuming interest is
compounded annually. $11,000 invested at an APR of 3.9% for 17 years.
a.
21,000
c.
21,079.34
b.
19,545.20
d.
28,000
3. Use the compound interest formula to compute the balance for the following account assuming interest is
compounded annually. $11,000 invested at an APR of 4.3% for 14 years.
a.
19,832.30
c.
17,596,02
b.
11,000
d.
9,789.35
4. Find the total value of the investment after the time given. $25,100 at 11% compounded annually for 8 years
a.
$57,843.90
c.
$57,824.11
b.
$47,188.00
d.
$57,858.38
5. Use the compound interest formula to compute the balance for the following account assuming interest is
compounded quarterly. $12,000 invested at an APR of 6% for 5 years.
a.
15,124.02
c.
16,162.26
b.
12,000
d.
17,000.58
6. Use the formula for continuously compounding to compute balance in the account after 1 year.
A $3000 deposit in an account with an APR of 3.3%.
a.
3100.65
c.
3000
b.
9900.00
d.
3033.33
7. Why is it so important that a statistical study uses a representative sample?
a. A non-representative sample only provides acceptable results when obtained using
convenience sampling.
b. Representative samples arenecessary because it is important that every sample of a given
size has an equal chance of being selected.
c.
Representative samples are more accurate than non-representative samples.
d.
If the sample fairly represents the population as a whole, then it is reasonable to make
inferences from the sample to the population.
Name: ________________________
ID: A
2
8. Briefly describe four common sampling methods.
a.
Box sampling; Normal sampling; Systematic sampling; Stratified sampling
b. Grouped sampling; Systematic sampling; Box sampling; Stratified sampling
c.
Simple random sampling; Systematic sampling; Convenience sampling; Stratified
sampling
d. Complex random sampling; Simple random sampling; Standard sampling; Convenience
sampling
9. 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.
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 makes sense. The experiment has both a control group and a treatment
group.
d.
The statement does not make sense. The vitamin C should be given to the control group,
not the treatment group.
10. What type of statistical study is most likely to lead to an answer to the following question?
Is magnetic therapy a more effective way to treat headaches than a Drug A or doing nothing at all?
a.
Experiment
b. Observational Study
11. What is the distinction between qualitative data and quantitative data. Give a few examples of each.
a. Quantitative data describe categories, while qualitative data represent counts or
measures. Brand names of shoes in a consumer survey and eye colors are examples of
quantitative data. Heights of students and quiz scores are examples of qualitative data.
b. Qualitative data describe categories, while quantitative data represent counts or
measures. Brand names of shoes in a consumer survey and eye colors are examples of
quantitative data. Heights of students and quiz scores are examples of qualitative data.
c. Quantitative data describe categories, while qualitative data represent counts or
measures. Brand names of shoes in a consumer survey and eye colors are examples of
qualitative data. Heights of students and quiz scores are examples of quantitative data.
d. Qualitative data describe categories, while quantitative data represent counts or
measures. Brand names of shoes in a consumer survey and eye colors are examples of
qualitative data. Heights of students and quiz scores are examples of quantitative data.
12. Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly
false). Explain your reasoning.
Your pie chart must be wrong, because when I added the percentages on your wedges, they totaled 124%.
a.
The statement does not make sense because pie charts are used primarily for relative
frequencies, which can add to any total degrees.
b.
The statement makes sense because pie charts are used primarily for relative frequencies,
so the total pie must always represent the total relative frequency of 100%.
c.
The statement does not make sense because pie charts are used primarily for relative
frequencies, which can add to any total percentage.
d.
The statement makes sense because pie charts are used primarily for relative frequencies,
so the total pie must always represent the total relative frequency of 360°.
Name: ________________________
ID: A
3
13. Determine whether the statement makes sense or does not make sense, and explain your reasoning.
I found a strong negative correlation for data relating the percentage of people in various countries who are literate
and the percentage who are undernourished. I concluded that an increase in literacy causes a decrease in
undernourishment.
a.
The statement makes sense. If a correlation exists between two variables, it can be
concluded that an increase or decrease in one variable causes an increase or decrease in
the other.
b.
The statement makes sense. The correlation between increased literacy and decreased
undernourishment is simply a coincidence.
c.
The statement does not make sense. Correlation is not necessarily causation.
d.
The statement does not make sense. There is no way for an increase in literacy to cause a
decrease in undernourishment
14. Determine whether the statement makes sense or does not make sense, and explain your reasoning.
In my data set of 10 exam scores, the mean turned out to be the score of the person with the third highest grade.
No two people got the same score.
a.
The statement does not make sense because there were no repeated scores, so the
distribution does not have a mean.
b.
The statement makes sense because the mean of a data set can be pulled far to the left or
right of the middle of the range of values by outliers.
c.
The statement does not make sense because the mean of a data set is always in the
middle of the range of values.
d.
The statement does not make sense because the mean of a data set is either near the
middle of the range of? values, or it is decreased by outliers in the data. The mean cannot
be increased by outliers.
15. Compute the mean of the following data set.
5.65 5.67 5.71 5.77 5.78 5.74
a.
5.67
c.
5.65
b.
5.77
d.
5.72
16. Find the mean for each data set.
a.
$57,748
c.
$31,874
b.
$57,924
d.
$37,435
17. Compute the median of the following data set.
5.65 5.67 5.71 5.77 5.78 5.74
a.
5.71
c.
5.77
b.
5.73
d.
5.15
Name: ________________________
ID: A
4
18. Find the median of the data set.
a.
30.9
c.
31.4
b.
33.1
d.
31.3
19. Compute the mode of the following data set.
5.65 5.67 5.71 5.77 5.78 5.74
a.
5.77
c.
no mode
b.
5.67
d.
5.78
20. The histogram to the shows the times between eruptions of a geyser for a sample of 300 eruptions. Classify the
distribution according to its number of peaks and its symmetry or skewness.
a.
three peaks, symmetric, wide variation
b.
one peak, symmetric, low variation
c.
two peaks, left skewed, wide variation
d.
one peak, right skewed, moderate variation
21. What is a standard score?
a. A standard score is a data value equal to the mean.
b. A standard score is the number of standard deviations a data value lies above or below
the mean.
c. A standard score is the distance between a data value and the nearest outlier.
d. A standard score is a data value that lies within one standard deviation of the mean.
22. How do you find the standard score for a particular data value?
a.
c.
b.
d.
23. What is the standard score of a test score of 65 when the mean is 75 and the standard deviation is 9?
a.
-1
c.
3.1
b.
-1.11
d.
1.11
Name: ________________________
ID: A
5
24. What is statistical inference? Why is it important?
a.
Statistical inference is the process of determining if the difference between what is
observed and what is expected is too great to be explained by chance alone. It is
important because we expect small deviations to occur by chance.
b.
Statistical inference refers to the process of collecting data about the sample. It is
important because it is rarely possible or plausible to collect data from an entire
population.
c.
Statistical inference refers to the process of designing and conducting an experiment. It is
important because well designed experiments are critical in order to obtain valid data
from a sample.
d.
Statistical inference is the process of making a conclusion about a population from
results for a sample. It is important because the goal of most statistical studies is to learn
something about an entire population.
25. Distinguish between an outcome and an event in probability. Choose the correct answer below.
a. Outcomes are the most basic possible results of observations or experiments. An event
consists of one or more outcomes that share a property of interest.
b.
Events are the most basic possible results of observations or experiments. An outcome
consists of one or more events that share a property of interest.
c. Outcomes and events are the same in probability.
d. Outcomes are the most basic possible results of events.
26. Give an example in which the same event can occur through two or more outcomes. Suppose you roll a fair,
six-sided die. Choose the correct answer below.
a.
The possible outcomes are rolling the number 1, 2, 3, 4, 5, or 6. The event of rolling an
even number will occur with the three outcomes 2, 4, and 6.
b.
The possible events are rolling the number 1, 2, 3, 4, 5, or 6. The outcome is the number
that is rolled.
c.
The possible events are rolling the number 1, 2, 3, 4, 5, or 6. The outcome of rolling an
even number will occur with the three events 2, 4, and 6.
d.
The possible outcomes and events are rolling the number 1, 2, 3, 4, 5, or 6.
27. Pizza House offers 2 different salads, 7 different kinds of pizza, and 6 different desserts. How many different three
course meals can be ordered?
a.
84
c.
82
b.
20
d.
15
28. An experiment consists of drawing 1 card from a standard 52-card deck. What is the probability of drawing a
queen?
a.
1/13
c.
1/2
b.
1/52
d.
1/4
29. Use the theoretical method to determine the probability of the following event.
Rolling a die and getting an outcome that is less than 3
a.
1/6
c.
1/2
b.
1/3
d.
2/7
Name: ________________________
ID: A
6
30. Use the theoretical method to determine the probability of the following event.
The next president of the United States was born on Sunday, Thursday, or Saturday.
a.
5/7
c.
10/21
b.
1/2
d.
3/7
31. Suppose that a jar contains 2 green marbles, 11 yellow marbles, and 7 white marbles. If one marble is selected,
determine the probability that it is white.
a.
1/10
c.
11/20
b.
7/20
d.
17/20
32. Halfway through the season, a basketball player has hit 77% of her free throws. What is the probability that her
next free throw will be successful? Use the relative frequency method to estimate the probability
a.
0.77
c.
0.50
b.
0.23
d.
0.73
33. Determine the probability of the given opposite event.
What is the probability that a 53% free-throw shooter will miss her next free throw?
a.
0.53
c.
0.23
b.
0.50
d.
0.47
ID: A
1
Advanced Math Pre/Post Test - Spring
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Decide if the following statement makes sense (or is clearly true) or does not make sense (or is clearly false).
The bank that pays the highest annual percentage rate (APR) is always the best deal
a.
The statement does not make sense because a higher APR always results in a lower
annual percentage yield than an interest rate with a lower APR
b. The statement does not make sense because, depending on how often the interest is
compounded, a lower APR could result in a higher annual percentage yield.
c.
THe statement makes sense because a higher APR always results in a higher annual
percentage yield than an interest rate with a lower APR.
2. Use the compound interest formula to compute the balance for the following account assuming interest is
compounded annually. $11,000 invested at an APR of 3.9% for 17 years.
a.
21,000
c.
21,079.34
b.
19,545.20
d.
28,000
3. Use the compound interest formula to compute the balance for the following account assuming interest is
compounded annually. $11,000 invested at an APR of 4.3% for 14 years.
a.
19,832.30
c.
17,596,02
b.
11,000
d.
9,789.35
4. Find the total value of the investment after the time given. $25,100 at 11% compounded annually for 8 years
a.
$57,843.90
c.
$57,824.11
b.
$47,188.00
d.
$57,858.38
5. Use the compound interest formula to compute the balance for the following account assuming interest is
compounded quarterly. $12,000 invested at an APR of 6% for 5 years.
a.
15,124.02
c.
16,162.26
b.
12,000
d.
17,000.58
6. Use the formula for continuously compounding to compute balance in the account after 1 year.
A $3000 deposit in an account with an APR of 3.3%.
a.
3100.65
c.
3000
b.
9900.00
d.
3033.33
7. Why is it so important that a statistical study uses a representative sample?
a. A non-representative sample only provides acceptable results when obtained using
convenience sampling.
b. Representative samples arenecessary because it is important that every sample of a given
size has an equal chance of being selected.
c.
Representative samples are more accurate than non-representative samples.
d.
If the sample fairly represents the population as a whole, then it is reasonable to make
inferences from the sample to the population.
Name: ________________________
ID: A
2
8. Briefly describe four common sampling methods.
a.
Box sampling; Normal sampling; Systematic sampling; Stratified sampling
b. Grouped sampling; Systematic sampling; Box sampling; Stratified sampling
c.
Simple random sampling; Systematic sampling; Convenience sampling; Stratified
sampling
d. Complex random sampling; Simple random sampling; Standard sampling; Convenience
sampling
9. 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.
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 makes sense. The experiment has both a control group and a treatment
group.
d.
The statement does not make sense. The vitamin C should be given to the control group,
not the treatment group.
10. What type of statistical study is most likely to lead to an answer to the following question?
Is magnetic therapy a more effective way to treat headaches than a Drug A or doing nothing at all?
a.
Experiment
b. Observational Study
11. What is the distinction between qualitative data and quantitative data. Give a few examples of each.
a. Quantitative data describe categories, while qualitative data represent counts or
measures. Brand names of shoes in a consumer survey and eye colors are examples of
quantitative data. Heights of students and quiz scores are examples of qualitative data.
b. Qualitative data describe categories, while quantitative data represent counts or
measures. Brand names of shoes in a consumer survey and eye colors are examples of
quantitative data. Heights of students and quiz scores are examples of qualitative data.
c. Quantitative data describe categories, while qualitative data represent counts or
measures. Brand names of shoes in a consumer survey and eye colors are examples of
qualitative data. Heights of students and quiz scores are examples of quantitative data.
d. Qualitative data describe categories, while quantitative data represent counts or
measures. Brand names of shoes in a consumer survey and eye colors are examples of
qualitative data. Heights of students and quiz scores are examples of quantitative data.
12. Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly
false). Explain your reasoning.
Your pie chart must be wrong, because when I added the percentages on your wedges, they totaled 124%.
a.
The statement does not make sense because pie charts are used primarily for relative
frequencies, which can add to any total degrees.
b.
The statement makes sense because pie charts are used primarily for relative frequencies,
so the total pie must always represent the total relative frequency of 100%.
c.
The statement does not make sense because pie charts are used primarily for relative
frequencies, which can add to any total percentage.
d.
The statement makes sense because pie charts are used primarily for relative frequencies,
so the total pie must always represent the total relative frequency of 360°.
Name: ________________________
ID: A
3
13. Determine whether the statement makes sense or does not make sense, and explain your reasoning.
I found a strong negative correlation for data relating the percentage of people in various countries who are literate
and the percentage who are undernourished. I concluded that an increase in literacy causes a decrease in
undernourishment.
a.
The statement makes sense. If a correlation exists between two variables, it can be
concluded that an increase or decrease in one variable causes an increase or decrease in
the other.
b.
The statement makes sense. The correlation between increased literacy and decreased
undernourishment is simply a coincidence.
c.
The statement does not make sense. Correlation is not necessarily causation.
d.
The statement does not make sense. There is no way for an increase in literacy to cause a
decrease in undernourishment
14. Determine whether the statement makes sense or does not make sense, and explain your reasoning.
In my data set of 10 exam scores, the mean turned out to be the score of the person with the third highest grade.
No two people got the same score.
a.
The statement does not make sense because there were no repeated scores, so the
distribution does not have a mean.
b.
The statement makes sense because the mean of a data set can be pulled far to the left or
right of the middle of the range of values by outliers.
c.
The statement does not make sense because the mean of a data set is always in the
middle of the range of values.
d.
The statement does not make sense because the mean of a data set is either near the
middle of the range of? values, or it is decreased by outliers in the data. The mean cannot
be increased by outliers.
15. Compute the mean of the following data set.
5.65 5.67 5.71 5.77 5.78 5.74
a.
5.67
c.
5.65
b.
5.77
d.
5.72
16. Find the mean for each data set.
a.
$57,748
c.
$31,874
b.
$57,924
d.
$37,435
17. Compute the median of the following data set.
5.65 5.67 5.71 5.77 5.78 5.74
a.
5.71
c.
5.77
b.
5.73
d.
5.15
Name: ________________________
ID: A
4
18. Find the median of the data set.
a.
30.9
c.
31.4
b.
33.1
d.
31.3
19. Compute the mode of the following data set.
5.65 5.67 5.71 5.77 5.78 5.74
a.
5.77
c.
no mode
b.
5.67
d.
5.78
20. The histogram to the shows the times between eruptions of a geyser for a sample of 300 eruptions. Classify the
distribution according to its number of peaks and its symmetry or skewness.
a.
three peaks, symmetric, wide variation
b.
one peak, symmetric, low variation
c.
two peaks, left skewed, wide variation
d.
one peak, right skewed, moderate variation
21. What is a standard score?
a. A standard score is a data value equal to the mean.
b. A standard score is the number of standard deviations a data value lies above or below
the mean.
c. A standard score is the distance between a data value and the nearest outlier.
d. A standard score is a data value that lies within one standard deviation of the mean.
22. How do you find the standard score for a particular data value?
a.
c.
b.
d.
23. What is the standard score of a test score of 65 when the mean is 75 and the standard deviation is 9?
a.
-1
c.
3.1
b.
-1.11
d.
1.11
Name: ________________________
ID: A
5
24. What is statistical inference? Why is it important?
a.
Statistical inference is the process of determining if the difference between what is
observed and what is expected is too great to be explained by chance alone. It is
important because we expect small deviations to occur by chance.
b.
Statistical inference refers to the process of collecting data about the sample. It is
important because it is rarely possible or plausible to collect data from an entire
population.
c.
Statistical inference refers to the process of designing and conducting an experiment. It is
important because well designed experiments are critical in order to obtain valid data
from a sample.
d.
Statistical inference is the process of making a conclusion about a population from
results for a sample. It is important because the goal of most statistical studies is to learn
something about an entire population.
25. Distinguish between an outcome and an event in probability. Choose the correct answer below.
a. Outcomes are the most basic possible results of observations or experiments. An event
consists of one or more outcomes that share a property of interest.
b.
Events are the most basic possible results of observations or experiments. An outcome
consists of one or more events that share a property of interest.
c. Outcomes and events are the same in probability.
d. Outcomes are the most basic possible results of events.
26. Give an example in which the same event can occur through two or more outcomes. Suppose you roll a fair,
six-sided die. Choose the correct answer below.
a.
The possible outcomes are rolling the number 1, 2, 3, 4, 5, or 6. The event of rolling an
even number will occur with the three outcomes 2, 4, and 6.
b.
The possible events are rolling the number 1, 2, 3, 4, 5, or 6. The outcome is the number
that is rolled.
c.
The possible events are rolling the number 1, 2, 3, 4, 5, or 6. The outcome of rolling an
even number will occur with the three events 2, 4, and 6.
d.
The possible outcomes and events are rolling the number 1, 2, 3, 4, 5, or 6.
27. Pizza House offers 2 different salads, 7 different kinds of pizza, and 6 different desserts. How many different three
course meals can be ordered?
a.
84
c.
82
b.
20
d.
15
28. An experiment consists of drawing 1 card from a standard 52-card deck. What is the probability of drawing a
queen?
a.
1/13
c.
1/2
b.
1/52
d.
1/4
29. Use the theoretical method to determine the probability of the following event.
Rolling a die and getting an outcome that is less than 3
a.
1/6
c.
1/2
b.
1/3
d.
2/7
Name: ________________________
ID: A
6
30. Use the theoretical method to determine the probability of the following event.
The next president of the United States was born on Sunday, Thursday, or Saturday.
a.
5/7
c.
10/21
b.
1/2
d.
3/7
31. Suppose that a jar contains 2 green marbles, 11 yellow marbles, and 7 white marbles. If one marble is selected,
determine the probability that it is white.
a.
1/10
c.
11/20
b.
7/20
d.
17/20
32. Halfway through the season, a basketball player has hit 77% of her free throws. What is the probability that her
next free throw will be successful? Use the relative frequency method to estimate the probability
a.
0.77
c.
0.50
b.
0.23
d.
0.73
33. Determine the probability of the given opposite event.
What is the probability that a 53% free-throw shooter will miss her next free throw?
a.
0.53
c.
0.23
b.
0.50
d.
0.47