Math Final Word Prob.

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1 cubic yard = ________________ cubic feet

point

1% of the loan amount

exponential growth.

A bank account with compound interest exhibits what we call

$0 (free)

A friend has a textbook that originally cost $150. The friend says that you can have it for 100% less than he paid for it. Your price will be

a quart

A liter is approximately equivalent to

the ball point of a pen

A millimeter is approximately the size of

statistically significant

A set of measurements in a statistical study unlikely to have occurred by chance are considered to be _______________.

120,000.

A town's population increases in one year from 100,000 to 110,000. If the population is growing linearly at a steady rate, then at the end of the second year it will be

1%

An account with an APR of 4% and quarterly compounding increases in value every three months (quarterly) by

circular reasoning

An argument in which the conclusion essentially restates the premise is an example of

conversion factor

An example of a __________ is 1 week = 7 days.

Bigville, where the divorce rate is 60%

Assume the national divorce rate is 30% (meaning 30% of marriages end in divorce). In which community is the difference from this national rate statistically significant?

#1- Pos. #2- Neg. #3- No Correlation #4- No Correlation

Classify the scatter plots as having a positive, negative, or no correlation.

an argument that uses the fallacy of limited choice

Consider the argument "Your lack of enthusiasm for soccer proves that you are not a sports fan." This argument is an example of

Loan 1 will have higher monthly payments, but you'll pay less total interest over the life of the loan.

Consider two mortgage loans with the same principal and the same APR. Loan 1 is fixed for 15 years and Loan 2 is fixed for 30 years. Which statement is true?

mandatory expenses.

Currently, the majority of government spending goes to

money that the government spends on programs that Congress must authorize every year

In terms of the U.S. budget, what do we mean by discretionary outlays?

most of the payment goes to the interest.

In the early years of a 30-year mortgage loan,

The graphics may distract you from the actual information being shown or may mislead you by making something look or seem better than it is.

Name and explain one way that graphics in the media might be misleading.

1000 meters

One kilometer is

144 square inches

One square foot is equivalent to

impossible.

P(event) = 0 means that the event is __________

certain.

P(event) = 1 means that the event is ____________

The probability of an event,

P(event), is always a number between 0 and 1.

premise

Set of facts or assumptions

FICA

Social Security and Medicare taxes

logic

Study of the methods and principles of reasoning

an argument that uses the fallacy of false cause

Suppose the fact that an event A occurs before event B is used to conclude that A caused B. This is an example of

It is used to fund other government programs.

Suppose the government collects $100 billion more in Social Security taxes than it pays out in Social Security benefits. Under current policy, what happens to this "extra" $100 billion?

At Least Once Rule (for independent events)

Suppose the probability of an event A occurring in one trial is P(A). If all trials are independent, the probability that event A occurs at least once in n trials is given by: P(at least one event A in n trials) = 1 - P(no events A in n trials) = 1 - [P(not A in one trial)]n

the house decreased in value over the past five years.

Suppose the value of a home changed by -20% over the past five years. This means that

$1000

Suppose you are in the 25% marginal tax bracket. Then a tax credit of $1000 will reduce your tax bill by

low risk, high liquidity, and high return

The best investment would be characterized by which of the following? (3)

dependent For dependent events A & B, P(A and B) = P(A) x P(B given A) where P(B given A) means the probability of event B given the occurrence of event A.

Two events are ____________ if the outcome of one event does affect the probability of the other event.

independent For independent events A & B, P(A and B) = P(A) x P(B).

Two events are ____________ if the outcome of one event does not affect the probability of the other event.

cannot If A & B are non-overlapping, P(A or B) = P(A) + P(B)

Two events are non-overlapping if they _________ occur together.

can If A & B are overlapping, P(A or B) = P(A) + P(B) - P(A and B)

Two events are overlapping if they __________ occur together.

argument

Uses a set of facts and/or assumptions to support a conclusion

divided by

What does the word per mean?

continuous compounding is infinitely many times per year APY is slightly higher

What is continuous compounding? How does the APY for continuous compounding compare to the APY for, say, daily compounding?

simple interest is based on original principal only compound interest is based on current principal (uses original principal plus interest already added)

What is the difference between simple interest and compound interest? Why do you end up with more money with compound interest?

heights of all elementary school children

Which data set would you expect to have the highest standard deviation?

The steady growth makes it easy to see any impending crisis long before the crisis becomes severe.

Which of the following is not true of any exponentially growing population? (Hint: think of the bacteria in the bottle parable)

because the sample needs to be representative of the whole population.

Why is it so important that a statistical study use a representative sample?

a higher monthly payment than a 30-year loan.

With the same APR and principal, a 15-year loan will have

all registered voters in the state of Texas.

You conduct a poll in which you randomly select 1000 registered voters from Texas and ask if they approve of the job their governor is doing. The population of this study is

normal distribution

a symmetric, bell-shaped distribution with a single peak which corresponds to the mean, median, and mode of the distribution

= compared value - reference value

absolute difference

A subjective probability is

an estimate based on experience or intuition.

A golden rectangle is

any rectangle whose long side is Φ times as long as its short side. - length and width have a ratio of Φ

Outcomes

are the most basic possible results of observations or experiments

A theoretical probability is - Based on what we expect to happen (in theory)

based on a model in which all outcomes are equally likely.

An empirical probability is

based on actual observations or experiments.

bias

characteristic of a statistical study in which the design or conduct of the study favors certain results

population

complete set of people or things studied

An event

consists of one or more outcomes that share a property of interest.

outlier

data value that is much higher or much lower than almost all other values

linear growth

grows by the same absolute amount in each unit of time

exponential growth

grows by the same relative amount in each unit of time

placebo

lacks the active ingredients of a treatment being tested in the study, but is identical in appearance

Expected value is a

long-term average. (value of event A) x P(A) + (value of event B) x P(B)

liquidity

measure of how easy it is to obtain cash from an investment

standard deviation

measure of the average of all deviations from the mean

is equal to the median.

In a normal distribution, the mean

fallacy

Deceptive argument in which the conclusion is not well supported by the premises

This does not make sense because volume cannot be measured in square feet.

Decide whether the following statement "makes sense" or "does not make sense." Explain your reasoning. I have a box with a volume of 2 square feet.

This does not make sense because distance ran cannot be measured in liters.

Decide whether the following statement "makes sense" or "does not make sense." Explain your reasoning. I know someone who can run 35 liters per second.

This does not make sense because stocks may outperform other types of investments one day, but they may also drop significantly another.

Decide whether the following statement "makes sense" or "does not make sense." Explain your reasoning. I'm putting all of my savings into stocks because stocks always outperform other types of investments over the long run.

This does not make sense because they would actually make 16.7% less.

Decide whether the following statement "makes sense" or "does not make sense." Explain your reasoning. If you earn 20% more than I do, then I must make 20% less than you do.

This does not make sense because compound interest is better than simple interest.

Decide whether the following statement "makes sense" or "does not make sense." Explain your reasoning. Simple Bank was offering simple interest at 5.25% per year for investments, which was clearly a better deal than the 5.25% compound interest at Compound Bank.

This does not make sense because Red Shuttle takes 90 minutes to the airport while Blue Shuttle only takes 80 minutes.

Decide whether the following statement "makes sense" or "does not make sense." Explain your reasoning. Sue prefers the Red Shuttle because it gets her to the airport in an hour and a half, while the Blue Shuttle takes 80 minutes.

This makes sense because usually you are going to end up paying more in interest rather than principal.

Decide whether the following statement "makes sense" or "does not make sense." Explain your reasoning. The interest on my student loan is only 7%, yet more than half of my payments are currently going toward interest rather than principal

does make sense started at 10%

Decide whether the following statement "makes sense" or "does not make sense." Explain your reasoning. The rate of return on our funds increased by 50% to 15%.

This statement does not make sense because they are not taking into consideration other factors that may make what they each pay in taxes differentiate.

Decide whether the following statement "makes sense" or "does not make sense." Explain your reasoning. We're both single with no children and we both have the same total (gross) income, so we must both pay the same amount in taxes.

pay extra toward principal

Discuss a way that a person paying an existing mortgage could reduce the total amount of interest paid and gain ownership of the home sooner (same mortgage - no refinancing).

units

For a quantity; Describes what is being measured or counted

higher risk = higher return

For an investment, how are risk and return usually related?

A) #1 B) #2 C) #3 D) #1

Four frequency histograms of data are shown below. Use them to answer the following questions. A) Which of the data sets is most symmetric? B) Which of the data sets is left skewed? C) In which data set will the mean lie to the left of the median? D) In which data set will the mean and median be approximately equal?

tax cuts are more important than other issues, governor will keep his promise, etc

Identify two hidden assumptions in the following argument. The current governor has campaigned for tax cuts. He gets my vote.

The Law of Large Numbers

If a process is repeated over many trials, the proportion of the trials in which event A occurs will be close to the probability P(A). The larger the number of trials, the closer the proportion should be to P(A). Says that if the trial is conducted many times, the empirical probability will get closer and closer to the theoretical probability.

feet3

If you multiply an area in square feet by a height in feet, the result will have units of

your tax is 25% of only a portion of your income, the rest is taxed at a lower rate.

If your taxable income puts you in the 25% marginal tax bracket,

a deficit of $1 million and a debt of $7 million.

In 2009, Bigprofit.com had $1 million more in outlays than in receipts, bringing the total amount it owed to lenders to $7 million. We say that at the end of 2009, Bigprofit.com had

less common than data values closer to the mean.

In a normal distribution, data values farther from the mean are

1.06 quarts/liter

The fact that 1 liter = 1.06 quarts can be written as the conversion factor

half the workers earn between $8.25 and $10.75

The lower quartile for wages at a coffee shop is $8.25 and the upper quartile is $10.75 What can you conclude?

$300

The price of a four-star meal, only $100 per couple decades ago, has increased 200%. The current price of a four-star meal is

120% of the old price

The price of a movie ticket increased from $10 to $12. This means that the new price is

may or may not be the person most Americans want to win, because the voting was subject to participation bias.

The show American Idol selects winners based on votes cast by anyone who wants to vote. This means that the winner

the relative frequencies in the categories in the pie chart.

The sizes of the wedges in a pie chart tell you

the spread of the data values around the mean.

The standard deviation is best described as a measure of

gross income.

The total amount of money that you receive is called your

1706^3 yards3

There are 1760 yards in a mile. Therefore, one cubic mile represents

sample statistics

numbers or observations that summarize the raw data

installment loan

paid off with equal regular payments

capital gains

profits from the sale of stock or other property

bond

promise to repay with cash in the future

tax deduction

reduces the taxable income

tax credit

reduces the total tax bill

= absolute difference/ reference value

relative difference

quantitative data

represents counts or measurements

A probability distribution

represents the probabilities of all possible events (usually in tabular form).

experiment

researchers apply a treatment to some or all of the sample members and then look to see whether the treatment had any effects

stock

share of ownership in a company

population parameters

specific characteristics of the population that a statistical study is designed to estimate

The house edge is

the expected value to the casino of a particular bet. A casino makes money because games are set up so that the expected earnings of players are negative, which means the casino's earnings are positive.

The gambler's fallacy is

the mistaken belief that a streak of bad luck makes a person "due" for a streak of good luck. Even though if you play "long enough" you will eventually win a game, you have to consider the continued losses that had been occurring. If you spend more money than what you won, you did not win at all.

standard score

the number of standard deviations a data value lies above or below the mean

statistics

the study of collecting, organizing, and interpreting data