Final Exam Review Spring 2012
Chapter 5
1.) You want to determine the eating habits of students at Arizona State University. Which of the following would make the best sample, and why? Also explain why each of the other choices would not make a good sample for this study
- Students who participate in sports
- Students majoring in public health
- Students in a single dormitory
- Students enrolled in a required mathematics class
2-4.) Identify the sampling method (simple random sampling, systematic sampling, convenience sampling, or stratified sampling).
2.) ESPN chooses its top 10 plays of the day by looking at responses from viewers who voluntarily send a text or a twitter message.
3.) Every 5th problem on your final is graded to determine your score.
4.) A taste test for a new soda is conducted at the entrance to the Chandler Ostrich Festival
5.) Determine whether the following study is observational or experimental. 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 National Cancer Institute study of 600 melanoma patients and 1000 cancer-free patients matched by age, sex, and race found that those having a single large mole had twice the risk of melanoma. Having 10 or more moles was associated with a 12 times greater risk of melanoma.
6.) Which of the following describes a study in which the researchers know which group of participants is receiving a placebo?
a.) Double-blind experimentb.) Observational study
c.) Single-blind experimentd.) Case-control study
7.) Does smoking cause cancer?
The following question would be best answered by which of the following types of studies
a.) Single-blind experimentb.) Case-control study
c.) Observational studyd.) Double-blind experiment
Refer to the Data
Hours in mall / Dollars Spent10 / 40
8 / 15
9 / 24
3 / 20
1 / 10
2 / 35
5 / 50
6 / 70
7 / 18
8 / 25
2 / 100
3 / 60
8.) Draw a scatter diagram for the data
9.) Find the equation of the line of best fit ______
10.) Find the correlation index ‘r’ ______
11.) Make a conclusion about the two variables
12.) Refer to the scatter diagram. Which of the following would be the best estimate for r (the correlation coefficient)?
13.) There is a 95% chance that between 53% and 59% of voters will vote for Congressman Bob in the next election. What do you know about the sample statistics and the margin of error of the survey?
a.)53% of the voters surveyed stated they will vote for Bob & the margin of error is 6%.
b.)56% of the voters surveyed stated they will vote for Bob & the margin of error is 6%.
c.)56% of the voters surveyed stated they will vote for Bob & the margin of error is 3%.
d.)59% of the voters surveyed stated they will vote for Bob & the margin of error is 6%.
14-18) Consider the following statements about a correlation. Is the correlation positive or negative? What might be the cause of the correlation? (Coincidence, direct cause, or a common underlying cause?
14.)The more time I spend lifting weights, the more you can see my muscles
15.)The more games the Diamondbacks win, the more jerseys they sell
16.)Whenever I get some cash from the ATM, my account balance decreases
17.)Whenever I see April 1st on the calendar, my heart beats faster and I panic
In what way(s) might the following studies be flawed (Guidelines for evaluating a statistical study)
18.) A comment box for “how well are we doing” placed in the store you work.
19.) A researcher is studying Christian beliefs by surveying members of his church.
20.) A recent magazine article determined that the Volkswagen Jetta is the most popular car on the road. A TV journalist decided to test the accuracy of the article with the following survey question. “Do you agree that the Volkswagen Jetta is the most popular car on the road?”
Chapter 6
6A
1)Compute the mean, median, and mode of the following data sets:
a)Body temperature (in degrees Fahrenheit) of randomly selected normal and healthy adults:
98.698.698.098.099.0
98.498.498.498.498.6
b)Golf scores from a recent WPGA tournament:
69707071737375767678
80818182838485868788
2)State whether you expect the distribution to be symmetric, left-skewed or right-skewed (think of outliers). Make a sketch and label the axes.
a)Among professional actors, a small number of superstars earn much more money than most other actors.
b)The prices of 32-oz containers of 20 different brands of laundry detergent.
c)The exam scores for 100 students when 40 got an F, 25 got a D, and 20 students got a C.
3)Find the range of the following data sets:
a) 0.150.020.160.370.22
2.03 0.270.921.072.38
b) 283650333040382668
c) 98.2108.7111.5135.4140.0216.0
6B
4)Give the five number summary for each data set:
a)The following data set gives the approximate lengths of Beethoven’s nine symphonies:
283650333040382668
b)Researchers conducted experiments with popular trees in which one group of trees was given fertilizer and irrigation. The weight in kilograms of this trees after the treatment are as follow:
2.030.270.921.072.381.161.86
5)Calculate the standard deviation of the following data sets:
a) 989295879690
659295939894
b) 155.8113.2144.8182.4156.0122.7
6)Apply the range rule of thumb to estimate the standard deviation for each of the two data sets from last problem.
a)
b)
6C
7)The scores on a psychology exam were normally distributed with a mean of 67 and a standard deviation of 8.
a)Find the z-score (standard score) for a data value of 83
b)Find the z-score (standard score) for a data value of 51
8)The resting heart rates for a sample of individuals are normally distributed with a mean of 70 and a standard deviation of 15. Use the 68-95-99.7 rule to find the percentage of heart rates in each of the following categories:
a)Less than 55
b)Less than 40
c)Less than 85
d)Less than 100
e)Greater than 85
f)Greater than 55
g)Greater than 40
h)Between 55 and 85
9)The scores on the verbal Graduate Record Exam (GRE) have a mean of 462 and a standard deviation of 120. The scores on the quantitative GRE have a mean of 584 and a standard deviation of 150. Assume the scores are normally distributed.
a)Find the percentile for a student who scored 606 on the verbal exam.
b)Find the percentile for a student who scored 494 in the quantitative exam.
Chapter 7
1-2 You roll two ordinary six-sided dice.
1) What is the probability of rolling a sum of 5?
2) What is the probability of NOT rolling a sum of seven?
3-6 You select one card from a standard deck of cards.
3) What is the probability you pick a heart or a ten?
4) What is the probability you pick a red card or a Queen?
5) What is the probability you pick an Ace or a Jack?
6) What is the probability you pick a club or a diamond?
7-8 A fair coin is tossed three times in succession.
7) What is the probability that you get one tail and 2 heads?
8) What is the probability that you get three tails?
9) The probability that a horse will win a race is 1/6. What are the odds that the horse will win the race?
10) The odds that a horse will win a race are 4/5. What is the probability that the horse will win the race?
11-12 A jar contains 3 red marbles, 8 blue marbles, 5 yellow marbles, and 2 green marbles.
11) If you randomly pick one marble, what is the probability that it is NOT blue?
12) You pick 2 marbles without replacement. What is the probability that you pick a red one and then a blue one?
13) At a horse race, the odds on Mighty Beast are given as 2 to 5. If you bet $50 and Mighty Beast wins, how much will you gain?
14) At a horse race, the odds on Mighty Beast are given as 5 to 2. If you bet $50 and Mighty Beast wins, how much will you gain?
15-16 There are 5 freshmen, 4 sophomores, 3 seniors, and 12 juniors in an art class.
15) The teacher randomly selects 2 students to present their artwork. What is the probability that the teacher picks a junior and then a freshman? (without replacement)
16) The teacher has the name of each student on an index card. She picks two index cards with replacement. What is the probability the teacher picks two seniors?
17-18 Mr. and Mrs. Jones plan to have 4 children.
17) What is the probability that they have 4 boys?
18) What is the probability that they have 3 boys and 1 girl?
19-20 A single six-sided die is thrown twice.
19) What is the probability you roll an even number and then you roll a 5?
20) What is the probability that you roll a 2 and then you roll a number greater than 4?
21) You roll a die five times. What is the probability that you roll at least one four?
22) You roll a die seven times. What is the probability that you roll at least one three?
23-24 A multiple choice test has 6 questions. Each question has 5 answers (a, b, c, d, and e).
23) How many ways can this test be answered?
24) If you guess on each question, what is the probability that you answer all of the questions correctly?
25) The Anime Club needs to pick a president, vice president, and secretary. If there are 30 people in the club, in how many ways can they pick a president, vice president, and secretary?
26) Using 22 flavors, how many different milkshakes can be created using 2 different flavors?
27) A teacher wants to choose five students to go to the board. If there are 23 students in the class, how many different sets of five could be chosen?
28) There are 10 horses in a race. In how many ways can they come in 1st, 2nd, and 3rd place?
29) The cafeteria is offering 5 salads, 4 entrees, 6 sides, and 3 desserts. How many different meals are possible if each meal must include 1 salad, 1 entrée, 1 side, and 1 dessert?
30) An outfit must consist of a skirt, a blouse, a hat, and a pair of shoes. How many outfits are possible if you have 7 skirts, 5 blouses, 3 hats, and 10 pairs of shoes?
Chapter 8 and Logarithms
1-4, State whether the statement is linear or exponential, and growth or decay.
1)The price of a gallon of gasoline is increasing by $0.03 per week.
2)The value of a car is decreasing by 10% per year.
3)The population of Chandler is increasing at a rate of 3% per year.
4)The value of your house is increasing by $2000 per year.
5)The doubling time of a population of fruit flies is 8 hours. By what factor does it increase in 24 hours? In 1 week?
6)The doubling time of a bank account balance is 20 years. By what factor does it grow in 40 years? In 100 years?
7)The initial population of a town is 10,000 and it grows with a doubling time of 8 years. What will the population be in 12 years? In 24 years?
8)A city’s population is growing at a rate of 3.5% per year. What is its approximate doubling time? By what factor will the population increase in 50 years?
9)The half-life of a drug in the bloodstream is 4 hours. What fraction of the original drug dose remains in 24 hours? In 48 hours?
10)The half-life of a radioactive substance is 400 years. If you start with some amount of this substance, what fraction will remain in 120 years? In 2500 years?
11)Urban encroachment is causing the area of a forest to decline at a rate of 7% per year. Use the approximate half-life formula to estimate the half-life. Use the exact half-life formula to find the half-life.
12)Inflation is causing prices to rise at a rate of 12% per year. Use the exact doubling time formula to find the doubling time.
13)In Israel, the birth rate is 2.38 births per 100 people per year and the death rate is .66 deaths per 100 people per year. Find the population growth rate as a percent.
14)In Sweden, the birth rate is 11.8 births per 1000 people per year and the death rate is 11.3 deaths per 1000 people per year. Find the population growth rate as a percent.
15)Consider a population that begins growing exponentially at a base rate of 6% per year and then follows a logistic growth pattern. If the carrying capacity is 80 million, find the actual growth rate when the population is 10 million, 50 million and 70 million.
16)The intensity of a baby cry is as loud as the softest audible sound. What is the loudness level in decibels?
17)The pH of seawater is 8.3. Find the hydrogen ion concentration of seawater.
18)How many more times intense is an earthquake with a magnitude of 7.1 than an earthquake with a magnitude of 5.2?
19) Find the value of
a) b) c)
20) Expand then simplify
a) b)
21)Condense to a single log then simplify
a) b)
22)Solve
a) b)
23)Solve
a) b)
24)Solve
a) b)
Chapter 9, Systems of Equations, and Linear Programming
1-3 There is a linear relationship between Shelly’s test grade and the amount of time she spends studying.
1. What is the independent variable? What is the dependent variable?
2. What is a reasonable domain?
3. What is a reasonable range?
4-6 Refer to the graph
4. What is the domain for men?
5. What is the range for men?
6. Find the rate of change for the number of people in the U.S. living alone between the years 1995 and 2010 for men.
7-9 Refer to the table
Time Practiced (Hours) / 10 / 2 / 7 / 5 / 12Bowling Score / 162 / 122 / 147 / 137 / 182
7. What is the independent variable?
8. What is the domain?
9. What is the range?
10-11 A pitchingmachine is loaded with 50 balls. When themachine is turned on, itpitches one ballevery 20 seconds. Write the equation of the line that shows the number of balls in the machine over a period of time.
10. What is the independent variable?
11. Write an equation of this function showing the number of balls in the pitching machine over a period of time.
12-17 The maximum speed of a semi trailer truck up a steep hill varies with the weight of its cargo. With 20 tons of cargo, it can maintain a maximum speed of 40 miles per hour. With 36 tons of cargo, its maximum speed drops to 32 miles per hour.
12. What is the independent variable? What is the dependent variable?
13. Write an equation for this linear function.
14. What is the rate of change and what does it mean in this problem?
15. What is the y-intercept and what does it mean in this problem?
16. At what load does a linear model predict a maximum speed of 0 miles per hour?
17. If the truck is carrying 85 tons of cargo, what will the speed of the truck be?
18. Graph the line or inequality
a) b) c) d)
19. Roses sell for $3 each and carnations for $1.50 each. If a mixed bouquet of 20 flowers consisting of roses and carnations costs $39, how many of each type of flower is in the bouquet?
20. A manufacturer produces two models of mountain bicycles. The times required for assembling are 5 hours for Model A and 4 hours for Model B. The times required for painting are 2 hours for Model A and 3 hours for Model B.
The maximum total weekly hours available in the assembly department and the paint department are 200 hours and 108 hours, respectively. The profits per unit are $25 for model A and $15 for model B. How many of each type should be produced to maximize profit?