Math Final
Is fairness criterion 4 satisfied?
no
The circular pattern in the floor is attractive because it exhibits the golden ratio.
The statement does not make sense because the golden ratio applies to rectangles and line segments, not circles.
The weights of babies born at Belmont Hospital are normally distributed with a mean of 6.8 pounds and a standard deviation of 7 pounds.
Does not make sense
Karen won a one-on-one election against each of the other candidates. She feels that she should win even though she lost in a runoff election.
This statement makes sense, by Fairness Criterion 2.
An economic indicator is increasing at the rate of 5% per year. What is its doubling time? By what factor will the indicator increase in 5 years?
What is its doubling time? 14 years (Type an integer or decimal rounded to the nearest tenth as needed.) By what factor will the indicator increase in 5 years? 1.28 (Type an integer or decimal rounded to the nearest hundredth as needed.) Is this formula valid in the case described? Yes
Wayne's bank charges a $1 service charge for every transaction. To save money, he withdraws $100 cash every other week instead of withdrawing $50 each week.
Makes sense
Decide whether the following statement makes sense (is clearly true) or does not make sense (or is clearly false). I know more of the names of the common fallacies in arguments than my father, so I can recognize fallacies better than he can.
does not make sense
I live in an apartment building that is 200 feet tall.
The statement makes sense because apartment buildings exist that are 200 feet tall.
Mike is the president of a large company with 12 divisions. He plans to use an apportionment method to decide how many staff support persons to assign to each division.
The statement makes sense.
A candidate has a plurality of the vote, yet lost the election using the Borda count method.
The statement makes sense because, using the Borda count method, the candidate with the most total points is the winner, regardless of who has a plurality of the vote.
State whether or is used in the inclusive or exclusive sense in the following proposition. For elective classes next semester i could take a literature class or a science class
Inclusive
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 negative correlation because air pressure tends to increase when altitude decreases.
I estimate that the probability of my getting married in the next 3 years is 0.7.
The statement makes sense. The statement is an example of subjective probability
Brandon discovered that his daily routine of buying a slice of pizza and a soda at lunch was costing him more than $2200 per year.
This statement makes sense because this would mean that a slice of pizza and a soda costs him about $6 a day.
My vacation travel cost a total of $2520, which I entered into my monthly budget as $210 per month.
This statement makes sense because when making a monthly budget, a prorated amount for expenses that don't recur monthly comma such as vacations comma should be included.
Automobile gas mileage decreases with tire pressure.
a positive This correlation is due to a direct cause because more gasoline is needed to roll a tire with lower pressure.
There's been only a very slight rise in our stock price over the past few months, but I wanted to make it look dramatic so I started the vertical scale from the lowest price rather than from zero.
The statement makes sense because reducing the range of the vertical axis to just fit the data will increase the relative size of the variation in the data.
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.
The statement does not make sense because the two people may not have the same adjusted gross income or taxable income.
I had originally suspected that an increase in variable E would cause a decrease in variable F, but I no longer believe this because I found no correlation between the two variables.
The statement makes sense. Originally a negative correlation was found, there is apparently no relationship between the variables
My bank paid an annual interest rate (APR) of 6.0% but at the end of the year my account balance had grown by 66.1%.
This makes sense, because the annual interest rate (APR) does not always match the annual percentage yield (APY).
In the following argument, identify the premise and conclusion, explain why the argument is deceptive, and identify the type of fallacy it represents. I will not give money to the tsunami relief organization. After I last gave to a charity, an audit showed that most of the money was used to pay its administrators in the front office.
1. Premise: After I last gave to a charity, an audit showed that most of the money was used to pay its administrators in the front office. Conclusion: I will not give money to the tsunami relief organization. 2. The conclusion is based on a personal allegation and uses ignorance about the truth to conclude the opposite. 3. appeal to ignorance, personal attack
I should have no trouble riding my bike up a road with a grade of 7%.
The statement makes sense because 7% is a very shallow grade and would be easy to travel up.
Is magnetic therapy a more effective way to treat headaches than Drug A or doing nothing at all?
Experiment
The argument involves some kind of fallacy. Identify the fallacy. When confronted with questions from the press about alleged scandals, a congressman replies that the allegations against him should be ignored since his accuser is part of a vast right-wing conspiracy.
Personal attack (ad hominem)
By turning off her lights and closing her windows at night, Maria saved 119% on her monthly energy bill.
The claim could not be true because her new monthly energy bill would be - 19% of the previous monthly energy bill. This is impossible since the bill cannot be negative.
The retail cost of a TV is 25% more than its wholesale cost. Therefore, the retail cost is ____ times the wholesale cost.
The retail cost is 1.25 times the wholesale cost.
The edge of this leaf has a fractal dimension of 1.34.
The statement makes sense.
No one can succeed in selling a product that will kill thousands of people per year.
The statement does not make sense because cars are sold every day and car accidents kill about 40,000 people per year.
My older child weighs 25% more than my younger child.
The statement makes sense because if the older child weighs 25% more than the younger child, then his weight is 1.25 times the younger child's weight, which is possible.
The rate of return on our fund increased by 50%, to 15%.
The statement makes sense because if the rate of return on our fund increased by 50%, to 15%, then the previous rate is 10%, which makes sense.
State whether it is possible for a deductive argument to be not valid with true premises and a false conclusion. If so, make a simple three-proposition argument that demonstrates your conclusion.
Yes, it is possible. Premise: All mammals breathe Premise: All lizards breathe Conclusion: All lizards are mammals
The doubling time of a population of flies is 8 hours. By what factor does the population increase in 32 hours? By what factor does the population increase in 2 weeks?
By what factor does the population increase in 32 hours? 2 Superscript 2^4 (Type exponential notation with positive exponents. Use integers or decimals for any numbers in the expression.) By what factor does the population increase in 2 weeks? 2 Superscript 2^42 (Type exponential notation with positive exponents. Use integers or decimals for any numbers in the expression.)
If interest rates stay at 5% APR and I continue to make my monthly $75 deposits into my retirement plan, I should have at least $30000 saved when I retire in 25 years.
The statement does make sense because I will have $44663.23 in my retirement account when I retire in 25 years.
Polls show that half the voters in our state plan to vote for Democrats in the House elections. Therefore, I can definitely expect half of our representatives to be Democrats.
The statement does not make sense because it is possible for district lines to be drawn in such a way that Democrats would be in the minority in more than half or less than half of the districts.
I read a book that had 10^5 words in it.
The statement makes sense because it is possible for a book to contain 100,000 words.
When I toss four coins, there are four different outcomes that all represent the event of three heads and one tail
This statement makes sense. There are four different ways the event can occur
Maria cut her 4-foot walking stick into two 2-foot sticks in keeping with the golden ratio.
The statement does not make sense because the golden ratio is approximately equal to 8/5, , which is not the proportion of the top half of the stick to the bottom half.
Decide whether each of the following statements makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. The payments we make to the electric company are a subset of the payments we make to the phone company.
The statement does not make sense because the two sets, payments made to the electric company and payments made to the phone company, are disjoint.
An earthquake of magnitude 8 will do twice as much damage as an earthquake of magnitude 4.
The statement does not make sense because the amount of damage depends on how the earthquake's energy is released.
Because Social Security is off-budget, we could cut Social Security taxes with no impact on the rest of the federal government.
Does not make sense
Javier takes a shower to save time. When he gets into the shower at 6:50, he is out by 7:10. When he used to take baths, it would take him a quarter of an hour.
Does not make sense
The population of city A is 25% less than the population of city B, so city A's population is _____% of city B's.
City A's population is 75% of city B's.
Describe one way in which both of the statements in the following pair could be true. A: The gun homicide rate is greater in country X than in country Y. B: The gun fatality rate is greater in country Y than in country X.
Country Y has a high gun suicide rate.
Decide whether the following statement makes sense (is clearly true) or does not make sense (or is clearly false). Your argument has no fallacies, so your conclusion must be true.
does not make sense
The amount of water the average person drinks in a year
180 gallons; assuming an average person drinks 4 pints per day
Half of the class consists of communication majors, and half of the class consists of men. Does it follow that one quarter of the class is male communication majors?
No
Three guests checked into a hotel and paid $51 for their shared room. A while later, the desk clerk realized that the room should have cost only $46, so she gave the bellhop $5 to return to the three guests. The bellhop realized that $5 couldn't be divided evenly among the three guests, so he kept $2 and gave $1 to each of the guests. It seems that each guest has spent $16 for the room (which makes $48) and the bellhop has $2, for a total of $50. Where is the missing dollar? Choose the correct answer below.
There is no missing dollar.
In a poll, 1 comma 1001 men in a country were asked whether they favor or oppose the use of "federal tax dollars to fund medical research using stem cells obtained from human embryos." Among the respondents, 46% said that they were in favor. Describe the statistical study.
1. All men in the country 2. The 1,001 men selected 3. The percentage of all men in the country who say that they are in favor 4. 46%
A company decided to expand, so it opened a factory, generating 455 jobs. For the 70 white-collor positions, 200 males and 200 females applied. Of the females who applied, 20% were hired, while only 15% of the males were hired. Of the 400 males applying for the blue-collar positions, 75% were hired, while 85% of the 100 females who applied were hired. Answer the questions below.
1. The percentages of women hired are higher than the percentages of men hired when the two types of positions are considered separately. 2. No 3. The data for each different type of position is being considered separately, leading to inaccurate conclusions. The paradox can be resolved by considering the data for both types of positions as a whole.
A computer randomly selects 600 names from a list of all registered voters. Those selected are surveyed to predict who will win the election for Mayor.
Simple random sampling
This argument involves some kind of fallacy. Identify the fallacy. One candidate favors eliminating affirmative action programs. The other candidate states: "My opponent doesn't think there's anything wrong with discrimination."
Straw man
Explain the meaning of the given statement, which contains a mulitple negation. Then answer the question that follows. Paul denies that he opposes the plan to build a new dorm. Does Paul support building a new dorm?
The first negation "opposes the plan" makes it seem that Paul would not support the new dorm. But the statement negates this negation, "Paul denies that he opposes the plan." Therefore, it seems that Paul supports the plan for the new dorm.
A toxic chemical decays with a half-life of 8 years, so half of it will be gone 8 years from now and all the rest will be gone 16 years from now
The statement does not make sense because after 16 years, the toxic chemical will decay by a factor of 0.25
The interest rate on my student loan is only 7%, yet more than half of my payments are currently going toward interest rather than principal.
The statement makes sense. The portions of installment loan payments going towards principal and toward interest vary as the loan is paid down.
he governor claims that the percentage of adults over 23 who have graduated from high school is greater than 88%, the national average.
1.The percentage of adults over 23 who have graduated from high school is 88% 2. The percentage of adults over 23 who have graduated from high school is greater than 88%. 3. There is evidence that the percentage of high school graduates exceeds 88% 4.There is insufficient evidence to conclude that the percentage of high school graduates exceeds 88%
The heights of male basketball players at a local college are normally distributed with a mean of 6 feet 3 inches and a standard deviation of 3 inches.
Makes sense
Suppose that you arrive at a bus stop randomly, so all arrival times are equally likely. The bus arrives regularly every 50 minutes without delay. What is the expected value of your waiting time?
The expected value of the waiting time is 25 minutes.
How many times greater is the intensity of sound from a concert speaker at a distance of 1 meter than the intensity at a distance of 4 meters?
The intensity of sound is 16 times as strong at 1 m as at 4 m. (Simplify your answer.)
The expected value to me of each raffle ticket I purchased is - $0.85.
The statement makes sense because a negative expected value implies that, averaged over many tickets, you should expect to lose $0.85 for each raffle ticket that you buy.
Linda used the permutations formula to determine how many possible relay orders could be made with the 10 girls on her swim team.
The statement makes sense because all selections come from the same swim team, each girl can be selected only once, and the order matters.
The principal vanishing point of the painting is so far away that it cannot be seen in the painting.
The statement does not make sense because the principal vanishing point is always part of the painting as that is what gives a painting perspective.
A mountain peak rises from sea level to a summit elevation of 2735 ft over a horizontal distance of 15840 ft. Find the grade of the peak.
The grade of the peak is 17%
The carrying capacity of our planet depends only on our planet's size.
The statement does not make sense because there are many factors that affect the carrying capacity that are not related to the size of the planet.
Wendy demanded a second election because she lost to Walt in a close plurality vote. In the second election, some of Wendy's supporters voted for Walt, but Wendy managed to win. (Assume other votes stayed the same.)
The statement does not make sense. If Walt is declared the winner of an election, and then a second election is held where he is ranked even higher than in the first election, Walt should also win the second election.
Both agencies conducted their surveys carefully, both asked the same question and found about the same proportion of "yes" responses, and both interviewed the same number of people. However, the margin of error was smaller for Agency A's survey than for Agency B's survey.
The statement does not make sense. The margin of error for two samples of the same size should be approximately the same.
Money in a bank account earning compound interest at an annual percentage rate of 3% is an example of exponential growth.
The statement makes sense because the money in the account grows by the same percentage, which is an example of exponential growth.
Give an explanation for the following fact that is more plausible than the given explanation. Fact: A football team in Division A has won four out of the last six championship games. Explanation: More Division A fans attend the championship game, so Division A teams have a home team advantage.
Winning four of six games is only one more win than the three wins that would be expected by pure chance.
Members of a reproductive health service are surveyed to determine whether American adults prefer abstinence, counseling and education, or morning-after pills for high school students.
Selection bias only
Explain how the following quote is ambiguous. Two jumbo jets with more than 350 people aboard nearly collided during a landing attempt.
Specify if there were 350 people on each jet or both jets combined.
If I double the amount of water in the cup, I'll also double the pH of the water in the cup.
The statement does not make sense because acidity is related to the concentration of positively charged hydrogen ions and not to the amount of liquid.
The two highways look like straight lines and they intersect twice.
The statement does not make sense because two straight lines cannot intersect more than once.
I made a distribution of 15 apartment rents in my neighborhood. One apartment had a much higher rent than all of the others, and this outlier caused the mean rent to be higher than the median rent.
The statement makes sense because an outlier with a large value increases the mean, but does not affect the median.
Suppose you build an architectural model of a new concert hall using a scale factor of 50. How will the surface area of the actual concert hall compare to the surface area of the scale model?
The surface area of the actual concert hall is 2500 times as great as the surface area of the scale model.
Suppose that the pairwise comparison method is used to determine the winner in an election. If there are 14 candidates, how many comparisons must be made?
91 comparisons
You are in the 10% tax bracket. The apartment rents for $1300 per month. Your monthly mortgage payments would be $2200, of which an average of $2000 per month goes toward interest during the first year. Determine whether renting or buying is cheaper in terms of monthly payments during the first year. Assume you are itemizing deductions.
It is cheaper to rent
Whether it's a problem in mathematics or something else, I always find it's best to complete the work by looking back to check, interpret, and explain my solution.
Makes sense
Consider the following statement about a correlation. State the correlation clearly (for example, there is a positive correlation between variable A and variable B). Then state whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause. Explain your answer. In a large resort city, the crime rate increased as the number of taxi cabs increased.
There is a positive correlation between the crime rate and the number of taxi cabs. This correlation is due to a common underlying cause because it is possible that, with an increase in tourism, both the crime rate and the number of cabs increase.
In 2007, 5,253,350 domestic cars and 2,365,063 imported cars were sold in the country.
1. Inaccurate reporting (by corrupt salesman), The recording of the sales data, The transfer of data, The recording type of car sold (imported or domestic), Other human error 2. No
The class is 70% women and 40% of the women have blond hair, so blond women comprise 70% times × 40% equals = 28% of the class.
The statement is true because blond women comprise 40% of women in the class and women comprise 70% of the class. Hence, blond women comprise 40 % times 70 % equals 28 %40%×70%=28% of the class
Your pie chart must be wrong, because when I added the percentages on your wedges, they totaled 124%.
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%.
A leprechaun places a magic penny under a girl's pillow. The next night there are 2 magic pennies under her pillow. Each night the number of magic pennies doubles. How much money will the girl have after 23 nights?
$83886.08
My bar chart contains more information than yours, because I made my bars three-dimensional.
The statement does not make sense because making the bars three-dimenional does not necessarily mean that information was added. It could mean that only the appearance of the graph was changed.
What do we mean by variables of interest in a study?
The items or quantities that the study seeks to measure
A newspaper reports that over 60% of adults avoid visits to the dentist because of fear.
The size of the sample, How respondents were chosen, The questions respondents were asked
I was unable to make a bar chart, because the data categories were qualitative rather than quantitative.
The statement does not make sense because bar graphs are commonly used to show data when the categories are qualitative.
A report claims that the returns for the investment portfolios with a single stock have a standard deviation of 0.57, while the returns for portfolios with 35 stocks have a standard deviation of 0.319. Explain how the standard deviation measures the risk in these two types of portfolios.
A lower standard deviation means more certainty in the return and less risk. Hence, the returns for portfolios with 35 stocks have less risk than the ones with a single stock.
A small town that grows exponentially can become a large city in just a few decades.
The statement makes sense because exponential growth leads to repeated doublings, making the population increase rapidly.
The probability of getting heads and tails when you toss a coin is 0, but the probability of getting heads or tails is 1.
The statement makes sense because heads and tails are the only possible outcomes and it is impossible to get both heads and tails on a single coin toss.
Jane wants near objects to look nearby and far objects to look far away in her painting, so she should use perspective.
The statement makes sense because perspective is a tool artists use to capture depth and volume on a two-dimensional canvas.
Exponential growth is found even in musical scales.
The statement makes sense because the frequencies of notes in a scale increase at a fixed relative growth rate, and exponential growth has a fixed relative growth rate.
Within the next decade, world population will grow by more than twice the current population of the United States.
The statement makes sense because the implied growth rate is reasonable.
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.
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.
A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, how many grains of wheat should be placed on square 20? ? Also find the total number of grains of wheat on the board at this time and their total weight in pounds. (Assume that each grain of wheat weighs 1/7000 pound.)
How many grains of wheat should be placed on square 2020? 524288 grains How many total grains of wheat should be on the board after the the grains of wheat have been placed on square 2020? 1048575 grains What is the total weight of all the grains of wheat on the board after the grains of wheat have been placed on square 20? 149.8 pounds (Round to the nearest tenth as needed.
I bought a fund advertised on the web that says it uses a secret investment strategy to get an annual return twice that of stocks, with no risk at all.
The statement does not make sense because investing in stocks is high-risk to get high returns, thus getting higher returns than stocks with this secret strategy must mean the fund advertised on the web is high-risk, not no risk.
After a recent NFL football game, the star player signed autographs for every person in attendance.
The statement does not make sense because it would take the player too much time to sign autographs for everyone.
A visitor arrived in a small, isolated town in need of a haircut. He discovered that there were exactly two barbers in town. One was well groomed, with splendidly cut hair; the other was unkempt, with an unattractive haircut. Which barber should the visitor patronize?
The unkempt barber
The Hill-Huntington method is superior to other apportionment methods because it requires more advanced mathematics.
The statement does not makes sense. The mathematics of an apportionment has no affect on the fairness of an apportionment method.
We began the trial with the null hypothesis stating that the toxic waste dump had no effect on disease rates among the residents nearby. The alternative hypothesis therefore stated that the toxic waste dump did have an effect on disease rates among the residents nearby.
The statement makes sense. If the conclusion that the waste dump had no effect is rejected, then it can be accepted that the waste dump did have an effect.
Determine whether the following study is an observational study or an experiment. If the study is an experiment, identify the control and treatment groups, and discuss whether single- or double-blinding is necessary. If the study is observational, state whether it is a case-control study, and if so, identify the cases and controls. A double-blind drug versus placebo study of 113 patients suffering from tinnitus (the perception of ringing in the ears) demonstrated the effectiveness of ginkgo biloba extract. The ginkgo treatment improved the condition of all the tinnitus patients.
Experiment; the treatment group is patients that received the drug and the control group is patients that received the placebo; double blind
Write the converse, inverse, and contrapositive of the following proposition. Of these four propositions, state which pairs are equivalent. If Teresa works in Texas, then she works in the South.
1. If Teresa works in the south, then she works in Texas. 2. If Teresa does not work in Texas, then she does not work in the south. 3. If Teresa does not work in the south, then she does not work in Texas. 4. Conditional and contrapositive, Converse and inverse
You are considering buying 12 gold coins that look alike, but you have been told that one of them is a heavy counterfeit. How can you find the heavy coin in three weighings on a balance scale?
1. Weigh eight coins at random, four on each side of the balance scale. 2. If the balance remains level, choose the un-weighed group of four coins; otherwise, choose the heavier of the weighed groups. 3. Divide the chosen group into two groups of two coins. Weigh the two groups and choose the heavier of the two. Weigh the two coins in the chosen group to find the heavy counterfeit.
Find the capital letters of the alphabet that have the following type of symmetry. Complete parts (a) through (d) below.
1. A, H, I, M, O, T, U, V, X, Y 2. C, D, H, I, O, X 3. H, I, O, X 4. H, I, N, O, S, X, Z
When I graphed the linear function, it turned out to be a wavy curve.
The statement does not make sense because a linear function has a straight-line graph.
After 100 years, a population growing at a rate of 2% per year will have grown by twice as many people as a population growing at a rate of 1% per year.
The statement does not make sense because both populations grow exponentially, not linearly.
Suppose you work for a company that manufactures cylindrical cans. Which will cost more to manufacture, a can with a radius of 3 inches and a height of 5 inches, or a can with a radius of 5 inches and a height of 3 inches? Assume that the cost of material for the tops and bottoms is $1.10 per square inch and the cost of material for curved surfaces is $1.00 per square inch.
The can with a radius of 5 inches and a height of 3 inches will cost more.
Identify the argument as inductive or deductive. Every coach must know his sport well. Marty Wright is a baseball coach, so Marty Wright knows baseball well.
Deductive
Decide whether each of the following statements makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. My professor asked me to draw a Venn diagram from a categorical proposition, but I couldn't do it because the proposition was clearly false.
The statement does not make sense because to draw a Venn diagram, the proposition can be either true or false.
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. Now that I've studied logic, I can always determine the truth of any statement by making a truth table for it.
The statement does not make sense. A truth table displays each possible set of truth values for the propositions being considered, but does not always make a definitive conclusion about the proposition.
Through the logic of deduction, I will show you that if you accept the truth of my premises, you must also accept the truth of my conclusion.
The statement makes sense. In a valid deductive argument, the conclusion follows necessarily from its premises.
Determine which of the following pair of surfaces is steeper. A roof with a pitch of 2 in 102 or a roof with a slope of 2/5
The roof with a slope of 2/5 is steeper
Your life expectancy is the major factor in determining how long you live.
The statement does not make sense because life expectancy is based on the current state of medicine and technology. If you have healthy habits and exercise each day, then you are more likely to live longer, regardless of your life expectancy.
In an election with only five candidates, each candidate received more than 35% of the votes.
The statement does not make sense because the candidates in an election cannot receive a combined total of more than 100% of the votes.
Our town is growing with a doubling time of 15 years, so its population will triple in 30 years.
The statement does not make sense because the population increases by a factor of 2^2 in 30 years
The price per gallon of gasoline has risen from only a quarter in 1918 to nearly $3 in 2009, thereby making it much more difficult for the poor to afford fuel for their cars.
The statement does not make sense because when inflation is taken into account, the two prices are quite comparable.
We can use the fact that radioactive materials decay exponentially to determine the ages of ancient bones from archaeological sites.
The statement makes sense because if the original amount of material is known and the half-life is known, then the amount of time can be found using the exponential model.
For the 30 students who took the test, the high score was 80, the median was 75, and the low score was 40.
The statement makes sense because it is possible that when sorting the 30 scores from low to high, the first value was 40, the highest value was 80, and 75 was halfway between the 15th and the 16th score.
The probability that two people in a randomly selected group will have the same last name is much higher than the probability that someone in this group will have the same last name as you do.
The statement makes sense because the coincidence that two people in a randomly selected group will have the same last name is more likely than the coincidence that someone in this group will have the same last name as you do.
The standard deviation for the heights of a group of 5-year-old children is smaller than the standard deviation for the heights of a group of children who range in age from 3 to 15.
The statement makes sense because the range of data for the heights of a group of 5-year-old children is smaller than the range of data for the heights of a group of children who range in age from 3 to 15.
Despite the fact that the new drug lowered blood pressure more than the old drug did in both the men and the women in the study, an overall analysis shows that the old drug was actually more effective.
The statement makes sense because there is no information given about the sampling method or about how the trials of the test were divided.
A woman bought a necklace for $800 and then sold it for $900. She bought it back for $400 and then sold it again for $700. How much did she gain or lose on these transactions?
She gained $400
Identify the hypothesis and conclusion in the statement, and state their truth values. Then determine whether the entire statement is true or false and explain why. IF 16 + 3 = 19, then America has a queen.
1. 16 + 3 = 19 2. America has a queen 3. true 4. false 5. The statement is false since the hypothesis is true and the conclusion is false
In the following argument, identify the premise and conclusion, explain why the argument is deceptive, and, if possible, identify the type of fallacy it represents. Everyone loves Shakespeare, because his plays have been read for many centuries.
1. Shakespeare's plays have been read for many centuries. 2. Everyone loves Shakespeare. 3. The argument is deceptive because the premise and conclusion essentially say the same thing, so the argument seems logical. 4. Circular Reasoning
Write the negation of the proposition. Then state the truth value of the original proposition and its negation. Earth is not the third planet from the Sun. Earth is not the third planet from the sun
1. earth is the third planet from the sun 2. false 3. true
Consider the following excerpt from the contract for the lease of an apartment. Landlord shall return the security deposit to resident within one month after termination of this lease or surrender and acceptance of the premises, whichever occurs first. Suppose the lease terminates on JulyJuly 3131, and the resident moves out of the apartment on JulyJuly 88. Answer parts a through c.
1. no 2. yes 3. yes
I found a nearly perfect positive correlation between variable A and variable B and therefore was able to conclude that an increase in variable A causes an increase in variable B.
The statement does not make sense because a correlation alone is not enough evidence to establish causality.
If John earns 20% more than Mary does, then Mary must earn 20% less than John does.
The statement does not make sense because if John earns 20% more than Mary, then Mary must earn approximately 16.7% less than John does.
Consider the following proposition. If Company A takes market share from Company B by manufacturing hybrid cars while Company B is still making SUVs, Company B is punished by the market. (a) What is the logical conclusion (if any) in the event that company A takes market share from Company B by manufacturing hybrid cars while Company B is still making SUVs? (b) What is the logical conclusion (if any) in the event that Company B is not punished by the market? (c) Can you draw any conclusion about what happens if Company A makes SUVs and Company B makes hybrid cars?
1. Company B is punished by the market. 2. Company A did not take market share from Company B. 3. There is no logical conclusion.
Suppose you magically tripled in size. That is, your height, width, and depth increased by a factor of 3. By what factor has your waist size? Examine a closed book. a. How many dimensions are needed to describe the book? Explain. b. How many dimensions describe the surface (cover) of the book? Explain. c. How many dimensions describe an edge of the book? Explain d. Describe some aspect of the book that represents zero dimensions.
1. Three dimensions are needed because the book has the form of a rectangular prism (box), and three coordinates are needed to locate a point in a rectangular prism (box). 2. Two dimensions are needed because the surface (cover) of the book is a plane object, and two coordinates are needed to locate a point in a plane object. 3. One dimension is needed because an edge of a book is a line segment, which is a one-dimensional object requiring only one coordinate to locate a point on a line. 4. A corner of the surface (cover), A corner of a page
The price of a computer component is decreasing at a rate of 9% per year. State whether this decrease is linear or exponential. If the component costs $60 today, what will it cost in three years?
1. exponential 2. $45.21
If I pluck this string more often, then it will have a higher pitch.
The statement does not make sense because plucking the string more often will not change the frequency, so the pitch will not change.
When we chart the price of milk in 1995 dollars we find that it has become slightly more expensive, but when we chart it in 1975 dollars we find that it has become cheaper.
The statement does not make sense because the same trend would be seen regardless of what kind of dollars are used.
The probability of drawing an ace or a spade from a deck of cards is the same as the probability of drawing the ace of spades.
The statement does not make sense because there is one card that is the ace of spades but more than one card that is either an ace or a spade.
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.
The statement does not make sense. Correlation is not necessarily causation.
The bank that pays the highest annual percentage rate (APR) is always the best deal.
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.
Baggage screening machines are 98% accurate in identifying bags that contain banned materials. Therefore, if the screening shows a bag that contains banned materials, then it almost certainly does.
The statement does not make sense because, depending on the proportion of true positives to total positives, the actual percentage of bags that show banned materials and actually have banned materials could be quite low.
In the last election in my home state, 48% of the people voted for a Democrat, and Democrats won 65% of our state's seats in the House of Representatives.
The statement makes sense because district lines could be drawn in such a way as to grant Democrats the majority in 65% of the districts.
The sides of triangle A are half as long as the corresponding sides of triangle B. Therefore, the two triangles are similar.
The statement makes sense because the ratios of the side lengths in the two triangles are all equal.
My freeway speed is the rate of change in my distance with respect to time.
The statement makes sense because the slope of a linear function is the change in the dependent variable divided by the change in the independent variable.
John's bedroom is a rectangular prism that measures 12 feet by 10 feet by 8 feet.
The statement makes sense because the volume formula for a rectangular prism (box) is the familiar length x width x height formula.
I can use a yardstick to find the area of my rectangular patio.
The statement makes sense.
The study found that more people were cured by the new drug than by the old drug, but the result was not statistically significant.
The statement makes sense. If the amount of the increase is small enough that it is likely to have occurred by chance, then the result would not be statistically significant.
In a survey of 1001 people, 701 (or 70%) said that they voted in a particular presidential election. The margin of error for this survey was 3 percentage points. However, actual voting records show that only 61% of all eligible voters actually did vote. Does this imply that people lied when they responded in the survey? Explain.
Based on the survey, the actual percentage of voters is expected to be between 67% and 73%, which does not include the 61% value based on actual voter results. If the survey was conducted properly, it is unlikely that its results would be so different from the actual results, implying either that respondents intentionally lied to appear favorable to the pollsters or that their memories were inaccurate.
Consider the following statement about a correlation. State the correlation clearly (for example, there is a positive correlation between variable A and variable B). Then state whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause. Explain your answer. When gasoline prices rise, sales of sport utility vehicles decline
There is a negative correlation between gasoline prices and sport utility vehicle sales. This correlation is due to a possible direct cause because sport utility vehicles require more gasoline than a smaller type of vehicle.
This argument involves some kind of fallacy. Identify the fallacy. After getting new dishes, I started to sneeze. I must be allergic to the new dishes.
False cause
In order to determine the opinions of people in the 18- to 22-year age group on regulating alcohol consumption consumption, researchers survey a random sample of 1000 college students in this age group.
Selection bias only
What are confounding variables, and what problems can they cause?
1. Items or quantities that are not intended to be part of the study 2. They can cause the study to favor certain results unexpectedly., They can cause incorrect conclusions to be drawn from the study.
Determine the truth of the premises of the following argument. Then assess the strength of the argument and discuss the truth of the conclusion.
1. The second premise is true, The third premise is true, The first premise is true 2. The argument seems moderately strong. The conclusion is false.
In the following argument, identify the premise(s) and conclusion, explain why the argument is deceptive, and identify the type of fallacy it represents. My little boy loves dolls and my little girl loves trucks, so there's no truth to the claim that boys are more interested in mechanical toys while girls prefer maternal toys.
1. Premise: My little boy loves dolls and my little girl loves trucks. Conclusion: It's not true that little boys are more interested in mechanical toys and girls prefer maternal toys. 2. The conclusion is drawn from an inadequate number of cases and uses ignorance about the truth to conclude the opposite. 3. hasty generalization, appeal to ignorance
My experiment proved beyond a doubt that vitamin C can reduce the severity of colds, because I controlled the experiment carefully for every possible confounding variable.
My experiment proved beyond a doubt that vitamin C can reduce the severity of colds, because I controlled the experiment carefully for every possible confounding variable.
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. My logical proposition is a question that you must answer.
The statement does not make sense because propositions are not questions.
I'm putting all my savings into stocks because stocks always outperform other types of investments over the long term.
The statement does not make sense because although stocks historically outperform bonds and cash over the long term, investing in stocks is high-risk and there is no guarantee that the investment will yield a high return.
If you toss a coin four times, it's much more likely to land in the order HTHT than HHHH. (H stands for heads and T for tails.)
The statement does not make sense because each outcome is equally likely since the probability of any single particular outcome is 1/2, so each set of outcomes have the same probability of
Wilma used a yard stick to measure the length of her kitchen to the nearest micrometer.
The statement does not make sense because a yard stick measures length in yards not micrometers. Therefore, the measurement will not be precise to the nearest micrometer.
Your bar graph must be wrong, because your bars are wider than the ones shown on the teacher's answer key.
The statement does not make sense because the width of the bars in a bar graph does not affect the accuracy of the graph. As long as the width of the bars on your graph represent the same category or interval as the teacher's graph, and the height of your corresponding bars are equal, then your graph is also correct.
I make only the minimum required payments on my credit card balance each month, because that way I'll have more of my own money to keep.
The statement does not make sense. It takes a very long time to pay off a credit card loan if only the minimum payments are made. This results in much more interest being paid.
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. Based on the testimonials of dozens of people who have lost weight following my diet, I will prove to you that my diet works for everyone
The statement does not make sense. Test cases never constitute a proof.
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.
The statement does not make sense. The control group should only receive a placebo, not another treatment.
The TV survey got more than 1 million phone-in responses, so it is clearly more valid than the survey by the professional pollsters, based on interview with only a few hundred people.
The statement does not make sense. The eight guidelines for evaluating a statistical study need to be reviewed before one study can be called more valid than another.
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. I weigh 110.3627 pounds.
The statement does not makes sense because no information about the precision of the measurement process is given, and it is highly unlikely that a person knows their weight to the nearest ten-thousandth of a pound.
Bank A was offering simple interest at 3.75% per year, which was clearly a better deal than the 3.75% compound interest rate at Bank B.
The statement does not make sense, because the compound interest pays more than the simple interest.
We found that these rare cancers were 700% more common in children living near the toxic landfill than in the general population.
The statement makes sense because the number of rare cancers found in children living near the toxic landfill is 8 times the number of rare cancers found in the general population, which is possible.
A $1 million error may sound like a lot, but when compared to our company's revenue it represents a relative error of only 0.1%.
The statement makes sense because the relative error is low. Thus, the $1 million dollar error is not very big when compared with the actual revenue.
When I calculated carefully, I found that it was cheaper for me to buy a house than to continue renting, even though my rent payments were lower than my new mortgage payments.
The statement makes sense.
I had a choice between a fixed rate mortgage at 6% and an adjustable rate mortgage that started at 3% for the first year with a maximum increase of 1.5 percentage points a year. I took the adjustable rate, because I'm planning to move within three years.
The statement makes sense. The monthly payment for the adjustable rate mortgage is guaranteed to be lower for the first three years of the loan term.
The pre-election poll found that a candidate would get 58% of the vote, with a margin of error of 3%, but he still lost the election
The statement makes sense. We can only be 95% confident that the actual percentage of people who vote for this candidate is between 55% and 61%. There is still a chance that the actual percentage is less than 50%.
In a preference schedule with three candidates and 23 voters, what is the total number of points awarded to the candidates using the Borda count weights?
The total number of points awarded to the candidates using the usual Borda count weights is 138 points
Two candidates for governor of a state differ in their accounts of the state's economy during the incumbent's term. The incumbent claims that during his four-year term the economy has improved, citing a rise in the median household income from $ 33 comma 000$33,000 to $ 34 comma 500.$34,500. The challenger claims that the economy has declined, citing that the buying power of families in the state has declined during the four years. Which of the following best explains how both candidates can be right?
Though the median household income increased, prices increased by a greater percent, meaning that in real terms the median income actually decreased.
My share of the federal government's debt is greater than the cost of a new car.
makes sense
Consider an experiment designed to determine the effectiveness of a new drug. The drug is given to participants in the treatment group, while participants in the control group receive a placebo. For the set of results described, discuss whether there appears to be evidence that the treatment is effective. 33% of those in the treatment group showed improvement; 55% of those in the placebo group showed improvement.
no