Final Exam Review
Describe the process of calculating a standard deviation. Give a simple example of its calculation (such as calculating the standard deviation of the numbers 2, 3, 4, 4, and 6). What is the standard deviation if all of the sample values are the same?
- Compute the mean of the data set. Then find the deviation from the mean for every data value by subtracting the mean from the data value. -Find the squares of all the deviations from the mean, and then add them together. -Divide this sum by the total number of data values minus 1. -The standard deviation is the square root of this quotient. -The standard deviation of the numbers 2, 3, 4, 4, and 6 is approximately 1.483. -If all of the sample values are the same, then the standard deviation is 0.
A man earned wages of $41,800, received $2500 in interest from a savings account, and contributed $2500 to a tax-deferred retirement plan. He was entitled to a personal exemption of $2900 and had deductions totaling $5480. Find his gross income, adjusted gross income, and taxable income.
- His gross income was $44,300. - His adjusted gross income was $41,800. - His taxable income was $33,420.
The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the mean, median, and mode of the listed numbers. 50 77 70 31 39 35 67 46 48 33
- The mean is 49.6 - The median is 47.0 - There is no mode.
Rephrase the argument, if necessary, so that the first premise has the form all S are P or no S are P. Then draw a Venn diagram to determine whether the argument is valid. If possible, discuss the truth of the premises and whether the argument is sound. Premise: All cliffs are tall. Premise: Two Foot High Cliff is a cliff. Conclusion: Two Foot High Cliff is tall.
- circle with tall circle with cliffs and x in middle -valid - the argument is not sound
What is energy? List three common units of energy. Under what circumstances do the different units tend to be used?
-Energy is what makes matter move or heat up. -Calorie; used to measure the energy the human body can draw from food. Joule; the international metric unit for energy. . Kilowatt-hour; used to measure electrical energy for utility bills.
Why is it so important to understand your personal finances? What types of problems are more common among people who do not have their finances under control?
-It is important to understand your personal finances because you need to know how much money you have and how much money you spend in order to find a way to live within your means. -People who do not have their finances under control suffer from financial stress, higher divorce rates, and other difficulties in personal relationships. They also suffer from higher rates of depression among a variety of other ailments.
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. My baby was vaccinated and later developed autism, which is why I believe that vaccines cause autism.
-My baby was vaccinated and later developed autism. -I believe that vaccines cause autism. -The argument is deceptive because it attempts to create a link between vaccines and autism. The premise of the argument does not fully support the conclusion. -False Cause
The following propositions have the form p and q. State p and q, and give their truth values. Then determine whether the entire proposition is true or false, and explain why. Oranges are vegetables and radishes are fruit.
-Oranges are vegetables -Radishes are fruit. -False -False -The entire proposition is false because p is false and q is false.
Consider two grocery stores at which the mean time in line is the same but the variation is different. At which store would you expect the customers to have more complaints about the waiting time? Explain.
-The customers would have more complaints about the waiting time at the store that has more variation because some customers would have longer waits and might think they are being treated unequally.
Define and distinguish among mean, median, and mode.
-The mean is the sum of all the values divided by the number of values. It can be strongly affected by outliers. -The median is the middle value in a data set. It is not affected by outliers. -The mode is the most common value in a data set. It is not affected by outliers.
Determine the truth of the premises of the following argument. Then assess the strength of the argument and discuss the truth of the conclusion. Premise: 3+7=10 Premise: 7+9=16 Premise: 5+5=10 Conclusion: The sum of an odd integer and an odd integer is an even integer.
-The third premise is true. The first premise is true. The second premise is true. - The argument is moderately strong. The conclusion is true.
Consider the distribution of exam scores (graded from 0 to 100) for 81 students when 39 students got an A, 25 students got a B, and 17 students got a C. Complete parts (a) through (d) below.
-There would probably be one peak because there are no obvious reasons why the exam scores would form different groups. -longest line starts on the left as straight line -The distribution would probably be left-skewed because many of the students got an A, and very few got a C. -The variation would probably be large because many students got an A, some got a B, and a small number got a C, and so the data are not clustered.
Pizza House offers 5 different salads, 4 different kinds of pizza, and 6 different desserts. How many different three course meals can be ordered?
120
The statement below connects two individual propositions with the word or. State the two individual propositions and, if possible, whether each is true or false. Then state whether the entire statement is true or false and explain why. 8×2=32 or 9+7=16.
1st Proposition 8x2=32 2nd proposition - 9+7=16 Is 1st true or false: false Is 2nd true or false. true Is statement true or false? The statement is true because the first proposition is false and the second proposition is true.
Use set notation to write the members of the following set, or state that the set has no members. Odd numbers between 0 and 28 that are multiples of 3.
3,9,15,21,27
A toll collector on a highway receives $4 for cars and $5 for buses. At the end of a 2-hour period, she collected $104. How many cars and buses passed through the toll booth during that period? List all possible solutions.
6 cars and 16 buses 16 cars and 8 buses 11 cars and 12 buses 1 car and 20 buses 21 cars and 4 buses 26 cars and 0 buses
What is a fallacy? Give examples of fallacies and describe how the argument is deceptive.
A fallacy is a deceptive argument. It is an argument in which the conclusion is not well supported by the premises.
What is a normal distribution? Briefly describe the conditions that make a normal distribution.
A normal distribution is a symmetric, bell-shaped distribution with a single peak. Its peak corresponds to the mean, median, and mode of the distribution. Its variation is characterized by the standard deviation of the distribution.
At age 25, someone sets up an IRA (individual retirement account) with an APR of 6%. At the end of each month he deposits $100 in the account. How much will the IRA contain when he retires at age 65? Compare that amount to the total deposits made over the time period.
After retirement the IRA will contain $199,149.07. The total deposits made over the time period is $48,000.
What is an index number? Briefly describe how index numbers are calculated and what they mean.
An index number provides a simple way to compare measurements made at different times or in different places. The value at one particular time or place is the reference value. The index number at any other time or place is given by index number=value/reference value×100.
Use the theoretical method to determine the probability of the following outcome and event. State any assumptions made. Tossing two coins and getting either one head or two heads
C. Assuming that each coin is fair and is equally likely to land heads or tails, the probability is 3/4.
Fill in the blank in the following statement. The population of city A is 23% less than the population of city B, so city A's population is _____% of city B's.
City A's population is 77% of city B's.
Which of the following are fallacies? Describe how each choice is deceptive. Select all that apply.
I placed the quartz crystal on my forehead, and in five minutes my headache was gone. The crystal made my headache go away. This argument is deceptive because it claims that because one thing happened before another, the first event caused the second event, but it doesn't prove that there is any connection between the two events. Your answer is correct. B. Society has an obligation to provide health insurance because health care is a right of citizenship. This argument is deceptive because the premise and conclusion essentially say the same thing. Your answer is correct. C. Company A makes the best pickup trucks in the world. More people drive Company A pickups than any other light truck. This argument is deceptive because the fact that a large number of people buy Company A pickup trucks does not necessarily mean that they are the best trucks.
Rewrite the following statement using a number in scientific notation. My new music player has a capacity of 430 gigabytes. (Recall that giga means billion.)
My new music player has a capacity of 4.3 x 10^11
What is statistical inference? Why is it important?
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.
To determine her heart rate, Britney divides up her day into three parts: morning, afternoon, and evening. She then measures her heart rate at 3 randomly selected times during each part of the day.
Stratified sampling
Make a truth table for the given statement. Assume that p, q, r, and s represent propositions. (not p) and p
T - F - F F - T - F
Explain whether the following argument is deductive or inductive. I have heard every CD released by a particular singer and they have been outstanding. Her next CD is bound to be good, so I will certainly buy it.
The argument is inductive because the premise is specific and the conclusion is general.
Explain whether the following argument is deductive or inductive. I have never found mail in my mailbox on a Monday. The Postal Service must not have Monday deliveries.
The argument is inductive because the premise is specific and the conclusion is general.
Use the appropriate compound interest formula to compute the balance in the account after the stated period of time $12,000 is invested for 10 years with an APR of 4% and quarterly compounding.
The balance in the account after 10 years is $17,866.36.
Use the two sets below to answer parts (a) and (b). dentists and women
The diagram correctly shows the two circles overlap because some women are dentists.
Find the monthly interest payment in the situation described below. Assume that the monthly interest rate is 1/12 of the annual interest rate. You maintain an average balance of $800 on your credit card, which carries an 18% annual interest rate.
The monthly interest payment is $12.00.
How many different choices of car does a person have if a particular model comes in 14 colors and 3 styles (station wagon, mid-size SUV, or full-size SUV)?
There are 42 different choices of car.
Fill in the blank. Will is 22% taller than Wanda, so Will's height is ____% of Wanda's height.
Will's height is 122% of Wanda's height.
Evaluate the following expressions. a. 104×106 b. 107×10−5 c. 10^6 / 10^2 d. 10^9 / 10^−3
a. 104×106=10^10 b. 107×10−5=10^2 c. 106102=10^4 d. 10910−3=10^12
Use the Venn diagram to the right to answer questions a. through d. below.
how many women at the party under 30? 10 how many men at the party are not under 30? 17 how many women are at the party? 39 how many people are at the party? 63 17 - 7 - 10 29
Use the appropriate compound interest formula to compute the balance in the account after the stated period of time $11,000 is invested for 7 years with an APR of 4% and quarterly compounding.
https://www.omnicalculator.com/finance/compound-interest
Identify the units of the following quantities. State the units mathematically and in words. Your average speed on a long walk, found by dividing distance traveled in miles by time elapsed in hours.
mi/hr miles per hour
What is a proposition? Give a few examples, and explain why each is a proposition.
"I did not take the pencil" is a proposition because it is a complete sentence that makes a denial. This is the correct answer. C. "The sky is purple" is a proposition because it is a complete sentence that makes an assertion. This is the correct answer. D. "The sun is shining" is a proposition because it is a complete sentence that makes an assertion.
Researchers design five survey questions to determine whether Norwegian citizens are happier than American citizens.
Yes, there is reason. It is not clear how the variable of interest is defined. Yes, there is reason. It is not clear how the variable of interest is measured.